AD NUMBER
THIS PAGE IS UNCLASSIFIED
UD
383
H57
1952
T P C H N I C A L
MEMORANDUM
ORO-T *160*
UNCLASSIFIED
Operational Requirements
U S ARMY m»UTARY HISTORY INSTITUTE
CARLISLE BARRACKS, PA 17013-5008
(or
an
OPERATIONS RESEARCH
OFFICE
•
The Johns Hopkins
University
INFANTRY
HAND WEAPON
By Norman Hitchman
Statistical Analysis by Scott Forbush and George Blakemore Jr.
This document is now unclassified, as shown on the
cover or title page, and all other markings found on any
pages are obsolete. If any photocopies are made of this
document, all markings, other than UNCLASSIFIED,
on each page should be obliterated so that there is no
misunderstanding of the current classification of any
information derived from it.
Operating Under
Contract with the
DEPARTMENT OF THE
ARMY
FORMATION
■*
The contents of ORO publications , including the conclu-
sions and recommendations, represent the Wews of ORO
and shou/d not be considered as having official Depart-
jnanf of the Army approval , either expressed or implied .
AWC Form 1 Army— CGSC— P2-0236— 9 Aug 51— 25M
vQ Udv KA
ciw contains informahon aflFec//ng /he na/iona/
defense of the United S fates wi/hin /he mean/ng of /he
Espionage Laws, Tide 7 8, U. S. C., Sections 793 and 794.
The /ransmi'ss/on or /he reve/adon of its contents in any
manner to an unauthorized person is prohibited by law .
ATION
1
[ON
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1 !
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SECUR!
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DOWNGRADED AT 3 YEAR INTERVALS:
... -!2 V
DOD DiR 5200.10
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THIS IS A WORKING PAPER
Presenting the considered results of study
by the ORO staff members responsible for
its preparation. The findings and analysis
are subject to revision as may be required
by new facts or by modification of basic
assumptions. Comments and criticism of
the contents are invited. Remarks should
be addressed to: ,
The Director
Operations Research Office
The Johns Hopkins University
6410 Connecticut Avenue
Chevy Chase, Maryland
' r
4 '
LIBRAS T
ARMY WAR COLLEGE
abstract taken by date
mm
UNUlftbMriLu,
OPERATIONAL REQUIREMENTS FOR AN INFANTRY HAND WEAPON
by
Norman A. Hitchman
Statistical Analysis
by
Scott E. Forbush
George J. Blakemore, Jr.
Of what should a rifle be capable in battle today? Since there is a
limit/as to how accurately the infantryman fires, can one increase hits
by giving him a rifle with new operational characteristics? ORO’s
Project BALANCE studied this by talcing data on how often, and by
how much, riflemen missed targets (as well as the distribution of
hits) at different ranges, by talcing data on the ranges of engagement
in battle, and by talcing data on the physiological wound effects of
shots with differing ballistic characteristics. The recommendation
is made that Ordnance proceed to determine the technological
feasibility of a weapon with operating characteristics analyzed iii
this memorandum. This follows from conclusions whjch are listed
only sketchily below:
Hit effectiveness using the M*1 is satisfactory only
* up to 100 yards and declines very rapidly to low
order at 300 yards, the general limit for battlefield
rifle engagements.
A pattern-dispersion principle in the hand weapon
• would tend to compensate for human aiming errors
and increase hits at ranges up to 300 yards.
Missiles, smaller caliber than now standard, ‘could
^ be used without loss in wounding effects and with
logistical advantage, and a great increase in hit
lethality could be effected by using toxic missiles.
Abstract page from: O RO" T- 1 60
LASSIF
(xM + 105 pp, 51 Figs., 11 Tables)
Received: 19 dune 1952
Proiect BALANCE
OPERATIONS RESEARCH OFFICE — The Johns Hopkins University
IMfBM CONlUd WITH 1 H I D ■ M I I W E H T OF THE ARMY
Log No.,
81938
Copy No
This Document contains information affecting the Nafiona/ Defense
of the United States within the meaning of the Espionage Laws,
Tit/e IS, U.S.C., Sections 793 and 794 . The transmission or the
reve/ation of its contents in any manner to an unauthorized person
is prohibited by law .
THIS ABSTRACT IS OF A WORKING PAPER
Presenting the considered results of study by the
ORO staff members responsible for its preparation.
The findings and analysis are subject to revision as
may be required by new facts or by modification
of basic assumptions. Comments and criticism of
the contents are invited. Remarks should be ad*
dressed to:
The Director
Operations Research Office
The Johns Hopkins University
6410 Connecticut Avenue
Chevy Chase, Maryland
Technical Memorandum ORO-T-160
^OPERATIONAL REQUIREMENTS FOR
AN INFANTRY HAND WEAPON
by
Norman A^[itdiman
Statistical Analysis
by
Scott E. Forbush
George J. Blake mo re, Jr*
LIBRARY
ARMY WAR COLLEGE
CARLISLE BARRACKS, PA.
Received: 19 June 1952
Project BALANCE
OPERATIONS RESEARCH OFFICE,
jV V|irj ■ - ^
The Johns Hopkins University.
Chevy Chase, Maryland
SECUI
immmorn
Unclassified
U2>
MS 7
oc LC&2. t L f
■ AYfY)
v£\<* b
\
Published
November 1952
by
OPERATIONS RESEARCH OFFICE
6410 Connecticut Avenue
Unclassified
ACKNOWLEDGMENT
The author gratefully acknowledges the
valuable assistance given by Col. E. M.
Parker, Project Chairman, in the prep-
aration of this study; especially were his
paraphrases welcomed, for they crystal-
lized areas of thought where otherwise
the author would have faltered.
CONTENTS
Page
ABSTRACT
ACKNOWLEDGMENTS
SUMMARY
Purpose — Assumptions — Discussion — Conclusions
Recommendations.
OPERATIONAL REQUIREMENTS FOR AN INFANTRY
HAND WEAPON
Introduction
COMBAT CASUALTY STUDIES
Former Studies — Lethality of the Rifle — Rifle
Bullet Hits as a Function of Range in Combat —
Man-Rifle Operations Studies.
TERRAIN VISIBILITY STUDIES
Range Requirements and Tactical Employment
of Hand Weapons — Map Analysis.
THE RIFLEMAN AND HIS WEAPON
Marksmanship: Tests and Analyses — The Pattern
Salvo Weapon — Full -Automatic Fire — Wound Bal-
listics: Missile Caliber, Mass, and Velocity.
LETHALITY
Weapons in General — The Rifle — Comparison of
an Ideal Dispersion Automatic with M-l Single-
Shot Fire — Can Lethality Be Increased?
THE DISPERSION WEAPON
Basis of Issue (T/O&E) — Training — Design
Feasibility.
5
7
10
15
25
31
ix
CONTENTS (Continued)
Page
A THEORY FOR DETERMINING RELATIVE EFFEC-
TIVENESS OF DIRECT FIRE WEAPONS
Method Used.
35
CONCLUSIONS
40
REC O MME NDATIONS
40
BIBLIOGRAPHY
42
APPENDIX
43
Analysis and Application of Results of Rifle-Range
Tests.
FIGURES
1. Comparison of Battlefield Visibility in Korea
anrj Ranges of Employment of the M-l Rifle. 10
2. Frequency Distribution for Ranges of Contin-
uous Visibility for Terrain Classes A, B, and C. 12
3. Method Used in Measuring Range of Visibility
on Maps. 14
4. Marksmanship Using the M-l Rifle. IV
5. Comparison of Lethality per Aimed Shot or
Burst for the M-l and the Salvo Automatic. 28
6. Rifle Marksmanship, Battlefield Visibility,
and Hit Probability in Combat. 37
7. Theoretical Distribution of Hits as Function of
Range for M-l Rifle and a Salvo-Type Hand Wea-
pon for Terrain Classes A, C. 38
8. Relative Effectiveness of M-l Rifle and Salvo
Automatic for Terrain Classes A, C. 39
UH iOl*
V i
Cf i
du
CONTENTS (Continued)
TABLES
1. Computed Distribution of Hits as Function
of Range R.
2. Relative Effects of M-l Single -Round Fire
and Salvo Fire as Function of Range for
Terrain Classes A and C.
Page
36
38
xi
SUMMARY
PURPOSE
The study reported upon in this memorandum was undertaken
for the purpose of determining the desirable operational char-
acteristics of a general purpose infantry hand weapon.
ASSUMPTIONS
It has been assumed that it is desirable to increase in both
number and rate the hits which may be inflicted on the enemy by
aimed small arms in the hands of the infantry.
It has been further assumed that it is desirable also to
increase the mortality of wounds caused by these hits.
DISCUSSION
In this examination of the basic infantry weapon, the rifle,
two commonly accepted considerations or premises were care-
fully scrutinized, and their bearing upon infantry operations
evaluated: 1) the time taken to hit enemy man targets is vital
in that hits should be inflicted as early and at as great a range
as possible; and 2) these hits should inflict significant injury —
should be at least immediately incapacitating (in some circum-
stances, lethal). The findings are generally affirmative with
respect to both propositions.
Study of combat records of operations, as well as field
investigations of the man-rifle combination, shows that much is
to be gained by increasing the hit capability of aimed rifle fire
at the common battle ranges, and that increasing the severity of
the hits is also to be sought. How men actually use the rifle in
combat, the ranges of engagement most frequently recurring
in battle, how terrain limits inter visibility of opposing firing
SECURI^^f^jMBfMRlFOetAATION
lines, and what is required ballistically to create physiologically
desirable wound effects on the enemy, are factors which have
been analyzed for the purpose of determining the operational
requirements of a general purpose hand weapon.
Study of the various factors involved has yielded a number
of independent but related and consistent determinations. Syn-
thesis has permitted comprehensive evaluation of the combat
actions bearing in concert upon effective employment of the
hand weapon.
Battlefield visibility data show why combat rifle fire is
actually so limited in range by normal terrain obstructions to
the line of sight as rarely to exceed 300 yd. Studies of the
manner in which gunshot wounds are incurred in battle suggest
that lesser -included ranges are in reality the important ones.
Measurements of marksmanship show that performance is of
a very low order beyond a range of 300 yd. Wound ballistic
data offer convincing evidence that small caliber, high velocity
missiles may be used profitably at such ranges, without loss
in wounding effects and with significant logistical gains.
The mutually confirmatory nature of the several findings
goes far to explain present rifle operations, and to suggest the
desirable characteristics for a general purpose infantry hand
weapon. The conclusions which follow have emerged.
CONCLUSIONS
1. The ranges at which the rifle is used most frequently in
battle and the ranges within which the greater fraction of man
targets can be seen on the battlefield do not exceed 300 yd.
2. Within these important battle ranges, the marksmanship
of even expert riflemen is satisfactory in meeting actual battle
requirements only up to 100 yd; beyond 100 yd, marksmanship
declines sharply, reaching a low order at 300 yd.
3. To improve hit effectiveness at the ranges not covered
satisfactorily in this sense by men using the M-l (100 to
300 yd), the adoption of a pattern-dispersion principle in the
hand weapon could partly compensate for human aiming errors
and thereby significantly increase the hits at ranges up to 300 yd.
4. Current models of fully automatic hand weapons afford
neither these desirable characteristics nor adequate alterna-
tives. Such weapons are valueless from the standpoint of
increasing the number of targets hit when aiming on separated
man- size targets.
2
ORO-T-160
SlWiT^^fPflfjy^TpTOiM ATIO N
5. Certain of tl
ccuracy observed
in the manufacture of current rifles and ammunition can be
relaxed without significant losses in over -all hit effectiveness.
6. To meet the actual operational requirements of a general
purpose infantry hand weapon, many possibilities are open for
panying increases in hit probability) at the ranges of interest.
Of the possible salvo or volley automatic designs,* the small
caliber, lightweight weapon with controlled dispersion char-
acteristics appears to be a promising approach. (Low recoil
of a small caliber weapon facilitates dispersion control.)
7. To create militarily acceptable wound damage at common
battle ranges, missiles of smaller caliber than the present stand-
ard .30 cal can be used without loss in wounding effects and with
substantial logistical and over -all military gains.
8. A very great increase in hit lethality can be effected by
the addition of toxic agents to bullet missiles.
RECOMMENDATIONS
1. It is recommended that the Ordnance Corps proceed to
determine the design or technological feasibility of developing
a hand weapon which has the characteristics cited in this
analysis, namely:
a. Maximum hit effectiveness against man targets
within 300 yd range. (This does not mean that the weapon will
be ineffective beyond this range. )
b. Small caliber (less than .30).
c. Wounding capability up to 300 yd at least equivalent
to the present rifle.
d. Dispersion of rounds from salvos or burst controlled
so as to form a pattern such that aiming errors up to 300 yd
^Current military usage of the two words salvo and volley is confused. By “salvo” the
Navy and Air Force generally mean, respectively, the simultaneous discharge of several
pieces, or the simultaneous release of a number of bombs; the Army usually employs the
word to indicate the successive firing of several guns within a single command unit.
“Volley” is commonly taken by all services to mean the simultaneous firing of a number
of rifles or guns, with the exception that the artilleryman often applies the word to the
independent (unsynchronized) firing of a certain specified number of rounds by each of
several associated pieces. What is discussed here and in the following pages is either
a simultaneous, or a high cyclic rate, burst , with the number of rounds per burst auto-
matically set rather than dependent upon trigger release. In the former design, con-
trolled nutation of the rifle muzzle would provide the desired shot dispersion or pattern;
in the latter, the scatter would be obtained and controlled by multiple barrels, a mother-
daughters type of projectile, or projection of missiles in the manner of a shotgun.
designs which will give desirable dispersion patterns (and accom-
ORO-T-160
j
3
SECURITY,
SECURITY-,
^FORMATION
Unclassified
will be partly compensated, and hit effectiveness thereby
increased for these ranges.
2. As one possible alternative to the current "volume of
fire" (fully automatic) approach to the problem of increasing
the effective firepower of infantry riflemen, it is recommended — subject
to tentative confirmation of design feasibility— that a rifle incor-
porating at least in principle the military characteristics here
proposed be manufactured for further and conclusive test.
jject
OPERATIONAL REQUIREMENTS FOR AN INFANTRY
HAND WEAPON
(INTRODUCTION
The subject of this study is of a basic nature for it applies
to the basic weapon of the basic branch— the rifle carried by the
infantry. Because the hand arm offers certain capabilities not
duplicated by any other means, and because it is basic to the
whole weapons system, the effectiveness of that weapon in battle
is a subject of first importance in any general consideration of
the whole fire system. It follows that any study directed toward
a comprehensive examination of the aggregate of weapons for the
purpose of designing and proportioning a “balanced" system
(the mission of Project BALANCE) may logically take a beginning
with this basic ground weapon.
Such an approach is, moreover, timely at the moment in the
sense that the NATO is confronted now by an urgent requirement
for standardization of a general purpose hand weapon for the
infantry. Thus, any information which may be cogently pertinent
to such weapons will have a bearing on an immediate problem of
some moment.
The study here presented has been carried out not only in
full recognition of the importance of improving the effectiveness
of infantry, but also in growing awareness that the task — even
though so basic in nature— is an exceedingly complex one. The
effort has thus far been only preliminary. Limited time, and
inadequate knowledge of basic unit operations in combat, have
restricted the degree to which the whole problem might be
examined. Consequently, no complete solution is offered by this
memorandum; rather, some analytical findings are presented,
which suggest the principles governing certain measures which
could be undertaken to improve infantry effectiveness with
respect to aimed rifle fire.
This memorandum bears directly upon the importance and
the use by infantry of aimed small arms fire in the front line
ORO-T-160
5
IMATION
Unclassil
tactical fire fight, but does not consider expressly the impor-
tance, the techniques or the effects of unaimed u covering fire 1 ’
delivered by small arms. The reason for directing the study
effort toward aimed fire is that the common arm of the infantry,
the rifle, is designed primarily for the aimed fire role; that is,
the weapon is designed expressly to afford a capability of directing
missiles at observed man-targets with high inherent precision,
in both offensive and defensive action. Delivery by such a weapon
of covering fire to neutralize or pin down the enemy and permit
friendly maneuver is tactically useful, but nonetheless amounts
to a secondary role for which design has provided only inciden-
tally, The important question at hand, therefore, is not so much
connected with the varying actual use of the present firearm as
with the need of the infantry to engage the close enemy effec-
tively by the use of aimed rifle fire, and with the feasibility of
incorporating in the rifle of general issue the capability of
answering this real requirement.
Recent ORO investigations in Korea have shed some light
on this subject by indicating quantitatively the comparative
importance of aimed and unaimed fire as related to offensive
and defensive operations. Generally, aimed fire plays a more
important part in defense than unaimed or volume fire, whereas
in the offensive, the reverse is true Almost irrespective of
the part played by the supporting weapons before or during the
final phase of close combat, the decision in each small tactical
battle rests ultimately in large measure with the infantryman
and his ability to use his hand weapon effectively. If hand-to-hand
fighting develops at all, decision thus rests almost entirely with
the infantry in this last time -phase of the tactical situation. To
attach importance to this aspect of battle is therefore logical,
and the attempt to maximize the capability of infantry in this
role cannot be misdirected effort.
The study has yielded suggestions for increasing infantry
effectiveness by improving the effects of aimed rifle fire. It
appears almost certain that future large-scale ground operations
will involve a numerically superior enemy and necessitate, at
first, a defensive strategy on our part. Morever, frequent
attempts to overrun infantry positions, with attendant close
combat, are to be anticipated. Thus, to increase each infantry -
highly desirable.
In the light of such considerations as these, it appears correct
to assume that: 1) it is desirable to increase in both number and
man's capability with respect to defensive rifle fire becomes
6
1
ORO-T-160
ified
rate the hits which may be inflicted on the enemy by aimed small
arms in the hands of the infantry; 2) it is also desirable to increase
the mortality from wounds caused by these hits.
The research effort has included examination of casualties
of past wars, studies of terrain as it limits battlefield visibility,
determination of the marksmanship of men, wound ballistics
requirements, actual use of the rifle in combat, and other
considerations bearing on military operational requirements
for the general purpose hand weapon. The determinations
arrived at from the study of present rifle fire and its effects
are presented in the following sections.
I
COMBAT CASUALTY STUDIES
Former Studies
Earlier work done by ORO on the defense of the individual in
combat, 1 and a preliminary study of the offensive capabilities
of the rifle, 2 yielded definite indications that rifle fire and its
effects were deficient in some important military respects, and
that further study of the problem would be necessary fully to
establish the facts. In these former studies it was found that,
in combat, hits from bullets are incurred by the body at random:
regional distribution of bullet hits was the same as for fragment
missiles which, unlike the bullet, are not "aimed. " Further,
it was found that exposure was the chief factor responsible for
the distribution of hits from bullets and that aimed or directed
fire does not influence the manner in which hits are sustained. 31
Stated briefly, the comparison of hits from bullets with those
from fragments showed that the rifle bullet is not actually better
directed towards vulnerable parts of th e body.
The discovery of these facts, along with evidence of prodi-
gious rifle ammunition expenditure per hit, strongly suggested
the need to extend the study of the rifle problem. The facts
known at this point also prompted one to regard with some
dubiety the employment of the present, highly accurate, pre-
cision-made rifle as a general purpose infantry weapon. It
should be noted, .however, that complete verification would not
suggest elimination of a precision long-range rifle to be used
‘Footnote numbers refer to publications listed in Bibliography.
Multiple hits on the same target are much less to be desired than a large number of
targets hit.
ORO-T-160
7
by some men highly skilled and selected for specialist opera-
tions, e. g. , snipers.
Lethality of the Rifle
As for the combat importance of hits from rifle bullets as
compared to other weapons in the ground system, historical
studies show that bullets have accounted for 10 to 20 percent
of all hits from all ground weapons in most battles, campaigns, and
wars of this century. 4 Although these figures qualitatively provide
a measure of the relative capability of hitting the opposed infantry-
man, they do not disclose capabilities with respect to severity of
injury. Of these two factors (simple wounding and extent of injury)
which characterize weapons effects, not much is known about either
in the sense of cost versus effect because ammunition expenditures
and corresponding casualty -producing effects are not usually known
with precision. On the other hand, aside from the closely related
machine gun, the rifle is the most lethal of all conventional ground
arms: its lethal index (ratio of kills to hits) exceeds 30 percent,
putting it above other weapons in capability of inflicting severe
injury.* The lethal index of the machine gun, of course, exceeds
that of the rifle because multiple hits increase over -all lethality.
For bullet lethality, the 30 percent figure given for the rifle would
be the closest approximation to single round lethality for all ranges
in battle .
Rifle Bullet Hits as a Function of Range in Combat
Knowledge of the ranges at which hits have been incurred in
past wars is sharply limited. Since this parameter is almost indis-
pensable to the military specialist or operations analyst in deter-
mining weapons effects, it is astonishing that greater efforts in the
past have not been directed toward gathering information of this
kind in combat operations.
*In this analysis, the figure 30 percent refers only to enemy weapons of World War II
type but since enemy rifles did not differ greatly from our own, the lethal index value
should approximate that of the M-l rifle. Strictly, lethal refers here to the bullet, rather
than the rifle, which is the launcher. What is meant is that a larger fraction of the total
bullet hits results in death than from hits from any other weapon. The explanation does
not lie in the manner in which rifle bullets are directed, since data show that bullet
hits occur on the body at random just as do hits from fragmenting projectiles and there-
fore their relatively high lethality is not connected with any bias in their distribution
over the body. The reason appears to be connected with the higher (and more nearly
constant) energy, on the average, than other missiles since they are discharged at short
ranges. Fragments, however, vary in energy from a maximum to zero, with the mean
value being relatively low because of the preponderance of small fragments per missile
burst and because of the rapid deceleration of particle velocities with range.
ORO-T-160
*
Unclassified
Only two studies exist which have reference to bullet hits as
a function of range in battle, and they are based on indirect and
possibly inaccurate measurements. Oughterson® analyzed expe-
rience on Bougainville in World War II and found that, of those
cases studied, almost all rifle bullet hits were received at ranges
less than 75 yd.* The Surgeon General recently examined the
wounded in Korea, and from a sample of 109 rifle bullet hits
suffered among members of the Turkish Brigade, the mean range
for these hits was found to be just over 100 yd.* It was noted,
however, that most of the hits occurred at ranges within 300 yd
and in a later section of this report these data along with data on
battlefield visibility will be given more extensive treatment.
Man-Rifle Operations Studies
The British AORG during World War II, and ORO in FECOM,
have both attempted to study part of the man-rifle complex by
interviewing experienced riflemen on their use of the weapon in
offensive and defensive combat actions. The British examined
officers and NCOs who had experience in the ETO 7 and ORO
examined men with experience in Korea. 8 The agreement of the
two independent studies is striking. For attack and defense in
European actions, it was found that about 80 percent of effective
rifle and LMG fire takes place at less than 200 yd and 90 percent
at less than 300 yd, according to the estimates made by the men
interviewed. About 90 percent of the LMG fire was at less than
300 yd.
Of 602 men questioned about use of the M-l rifle in Korea,
87 percent said that at least 95 percent** of all their firing was
done at targets within 300 yd range (day time offensive fighting)."
For day time defensive fighting, 80 percent of the men said that
rifles were used at 300 yd or less. Figure 1 shows the frequency
in which rifles are used as a function of range, based on responses
of interrogated infantrymen. The approximate correspondence of
the curves in the Figure indicates that the use of the rifle is to at
least some extent dependent upon battlefield terrain features as
they affect visibility.*** Although it is freely acknowledged that
the use of data derived from judgments of the men about the use
of their basic arm may be subject to question, the validity of the
*
This figure is perhaps atypically low because it refers to jungle fighting in which
^visibility was abnormally restricted.
The men were asked to give the outside limit of 95 percent of their firing in order to
eliminate those rare shots which might be fired at long ranges without expectation of
^ hitting the target.
See section on battlefield visibility.
aamfaS£CRFT iiirnniii—i
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opinion survey has been substantiated by a more recent Korean
study conducted in combat areas . 5 Also, as mentioned earlier,
the analysis made by AORG tends to support the conclusion that
Fig. 1 — Comparison of battlefield visibility in Korea and ranges of
employment of the M-l Rifle.
the infantry basic weapon is actually used, on the average, at
shorter ranges than commonly believed.
TERRAIN VISIBILITY STUDIES
Range Requirements and Tactical Employment of Hand Weapons
Despite the important role of infantry support weapons (artil-
lery, tactical aviation, armor, and others), the entire ground
weapon system hinges in many important ways upon those weapons
which depend for their effective employment upon ground obser-
vation of the target . These are the direct-fire and observed-fire
weapons ; they are elemental, basic, and indispensable to the
infantry-artillery-armor team.
Unclassifie
ORO-T-160
wmr TnfohmatiS
I I
tf**.
3d
For infantry, the basic direct fire weapon is the rifle— it is
the common denominator upon which the entire fire system is
designed, both physically and tactically. Yet all direct-fire
weapons suffer a major weakness in that essential observation
for their effective employment may be obscured by weather
conditions, prevented by darkness or— more importantly and
quite unavoidably— interrupted by terrain features. This inter-
ruption of the line of sight is one of the principal military effects
of terrain, for the ranges at which points on the ground are inter -
visible are related to the employment and general effectiveness
of these direct-fire weapons. Accordingly, terrain limitations to
continuous visibility on the battlefield should dictate to a consid-
erable degree the actual design and employment of direct-fire or
observed-fire weapons. A study of this subject which was under-
taken by Project BALANCE and which is covered in detail in a
separate report, 10 has yielded formulary expressions for the
relationship between the opening range of engagement for riflemen
and the range at which man-targets can be seen. Particularly with
respect to the rifle, the study is basic in its concept and possibly,
for the first time, data have been obtained which constitute a
reasonable quantitative basis for determining the actual range
requirements and tactical employment of a general-purpose
hand arm.
Because of the importance of these findings to the infantry
weapons problem, they should be studied carefully in conjunction
with the work presented here on operational requirements for an
infantry hand weapon.
Map Analysis
Topographical map studies of a number of large scale (1:25,000)
maps of various countries in the world have shown that it is pos-
sible to predict, with reasonable accuracy, the probability of being
able to see continuously for a given distance from a random point
within the area. 10
For the infantry study, the procedure used in the map analyses
was to measure the continuous ranges of visibility between infantry-
men, with the position of one man (the defender) being at ground
level (foxhole or prone) and the approaching enemy being an erect
human target five feet high. This factor was chosen to set realistic
limits on the range of iiit$r visibility betwqen^opposing forces. The
unclassified
ORO-T-160
11
validity of the map readings was verified by actual terrain meas-
urements* and the findings are in general agreement with limited
combat data from the Korean experience and ETO experience dur-
ing World War II.**
From the map study, it was found that all the types of terrain
so far considered fall into one of three categories which are illus-
0 500 1000 1500
R (YD)
Fig* 2 — Frequency distribution for ranges of continuous visibility for Terrain Classes
A, B, and C. (Probability of seeing man-targets at ranges greater than R yards from a
random point within the area covered by the map analysis.)
* Tests were conducted on the battlefield area of Gettysburg in which a small party of
ORO analysts checked map predictions by actually walking over the terrain in accord-
ance with the map bearings and measuring the distance of intervisibility. In every
instance, distances of continuous visibility were found to be less than the distances
predicted by map measurement because of terrain features and obstacles not shown on
maps. Map readings were considered, therefore, to represent maxima.
The mean ranges of visibility from map analyses of Korea and Normandy show remark-
able agreement with limited combat knowledge of ranges of engagement between
riflemen and between tAnks. In Korea, the frequency of ranges for bullet hits agreed
with the frequency of ranges for visibility. For World War II tank battles, both Peterson
of Ballistics Research Laboratory and ORO (Ref. 10) have shown that ranges of engage-
ment for tanks correspond with ranges of visibility in the battle areas as determined
from map analysis. These two samples of combat data tend to validate the use of the
map data for predicting range requirements.
ORO-T-160
*
linin'* SECRET-
1
sified
trated by the three curves in Fig. 2. The frequency distribution
for Type A terrain is typical for a country like the Saint-Lo area
in Normandy, where visibility is sharply limited by the masses of
hedgerows, small cultivated fields, orchards, and the nature of
the terrain itself. Type A also describes rugged, mountainous
terrain like Korea. The distribution curve for Type C describes
relatively open country where the topography is gently rolling and
large, open, cultivated areas exist. Type B is intermediate between
the two extremes cited and describes an average type of cultivated
countryside.
The importance of these data to the infantry study is related
to the range requirements for infantry weapons and, as shown in
Fig. 2, 95 percent of all observations include ranges which are much
less than the range capabilities of many of the infantry direct fire
weapons. The implication that such weapons may be over -designed
is appreciated when it is considered that the rifle alone has a
maximum range capability of 3,500 yd.
The following description of the procedure used in the map study
is presented so that the practical application of the data may be
recognized.
Figure 3 shows diagrammatic ally a corner section of a 1:25,000
map. The method of measurement was adopted from a suggestion
by Peterson of Ballistics Research Laboratory who used map grid
lines as guides for sampling any given terrain.
The analysis of each map is begun at Point A (northwest corner).
Proceeding along the east-west grid line, the distance is measured
from the edge of the map to the point where an erect (five feet)
infantryman would just be obscured from the sight of a defending
prone infantryman at Point A. In this case, the crest of a hill
(contour) is the factor which obstructs visibility. After recording
the distance A to B, the next point of obscuration is measured by
proceeding along the grid line from Point B to Point C where a
railroad embankment interrupts the line of vision. Distance BC
is then recorded and so on along the grid line to the far edge of
the map. It will be noted that a house or building limits visibility
at Point D and woods limit vision at Point E.
After all horizontal grid lines are measured in this way, the
same method is used on all vertical grid lines. Then all the obscu-
rations from one map are used to plot a frequency distribution.
Examples of such frequency distribution have been given already
in Fig. 2.
ORO-T-160
13
SfCftET
1 ^
r j'
Although the frequency tlistri^utioh curyes yield predictions as
to the probability of seeing man targets at Range R, from any ran-
dom point on the terrain, it may be argued that infantrymen are
not randomly located along the front but actually take up positions
which have been selected for point of advantage (for example, high
ground in the defence). So far as this is true for small units such
as squads and platoons especially in defensive positions, such biases
as a result of the placement of men are not systematic, and when
division or corps fronts are considered, the density of men and
their positions across a broad front can be considered to be more
Edge of Map
Starting at the northwest corner of the map one looks from the point A / where the first hori-
zontal grid line begins, along that grid line to the point B where, because he has gone over
the crest of a hill, the standing infantryman (the target) ceases to be visible. The distance
AB is measured and recorded. Next, starting from B, one finds that the target is continu-
ously visible until the railroad embankment at C causes obstruction to view; the distance
BC is then measured and recorded. Similarly, starting from the top of the embankment, it is
clear that there is no obstacle until one reaches the house at D; CD is measured and
recorded. Next the distance DE is recorded; then, starting from the eastern edge of the
wood, the distance to the next obstruction is measured; and so on across the map to the
right margin. After all horizontal grid lines have been followed in this way, one starts
again at the northwest corner and reads from F down the first vertical grid line and all the
other grid lines. All the readings obtained in this way are used to plot a frequency distri-
bution. Figures 2 through 7 are examples of such frequency distributions.
14
ORO-T-160
or less uniform. Thus, in relation to terrain, their position is
more nearly random. Also, no systematic selection of ground is
permitted either side during a battle, since position, which is
fluid and constantly changing, is dependent upon the whole battle
situation and not just upon ground features. Therefore, the random
selection on a map of a battlefront in any given terrain should pre-
dict the actual ground condition of the battlefield. In general, it is
felt that men move in battle in a more or less random manner, so
the data obtained in the visibility study are reasonably valid for
predicting the probability of seeing targets over any area, particu-
larly since the method used measured the type of movement used
by troops in battle, that is, from cover to cover.
Employing this method, map studies of Canada, France, Germany,
Korea, North Africa, and the US, to a total of some 18,000 readings,
showed that 70 percent of the ranges at which an erect human target
can be seen by a defending prone rifleman are less than 300 yd (and
that 90 percent are less than 700 yd).
Since range requirements exert a considerable if not dominating
influence upon such characteristics as weight, caliber, and missile
velocity, the data from the map analyses have a very important
bearing upon the design of an infantry hand weapon. Comparing the
range analysis data with the maximum range of the present M-l
rifle (3,500 yd), and its design for incapacitating clothed personnel
up to 1,200 yd, it may be concluded that the effective rang es of the
greater part of infantry hand weapons cou ld be reduced materially
to an order suggested by the terrain analysis. (A reduction of the
range of the rifle for maximum effectiveness up to 300 yd does not
mean that the weapon would not be effective at ranges beyond this. )
THE RIFLEMAN AND HIS WEAPON
Marksmanship: Tests and Analyses
The preceding sections have described, to some extent, certain
major factors dictating the actual operational requirements for the
general-purpose hand arm of infantry. Since marksmanship obviously
plays a major role in the over -all effectiveness of hand weapons em-
ployment in the military situation, the measure of the varying capa-
bilities of combatants to use their weapons with tactical effectiveness
becomes, along with target visibility, a significant parameter in the
whole infantry study.
To provide meaningful data on this subject, field tests were con-
ducted at Fort Belvoir, Virginia, where 16 expert riflemen (highest
ORO-T-160
15
grade) and 16 marksmen (lowest qualified grade) were used in a
series of experiments designed to simulate some of the conditions
of combat. The 32 men were divided into groups for two sets of
tests. Firing the M-l rifle from the prone position, using battle
sights, they shot at a man- silhouette target operated on a tran-
sition-type range, at distances of 100-300 yd. Mounted behind the
silhouette was a 6 foot high by 12 foot wide screen; on this could be
measured the dispersion of rounds. The target butts were draped
with OD cloth so that short rounds, not striking the target, could
also be recorded. (These experiments and the results are described
in detail in the Appendix. )
Further data were procured from a range test on automatic
rifles at Fort Benning, Georgia.*
In the tests at Belvoir, a variety of conditions was imposed on
the participants chiefly by changing the time of target exposure
and imposing forms of psychological duress. It was found that
best results were obtained when single rounds were fired on an
individual basis at-sfatic man-size targets. Marksmanship
declined when group firing (4-man groups) was performed at the
same targets. With slight psychological load, in the form of
limited target exposure time and random order of presentation
at varying ranges, a further decline in effectiveness was noted.
Hit probability as a function of range for both grades of riflemen
is shown in Fig. A4 (Appendix).
Significant results from these analyses are: (a) hit probability
is high for both grades of riflemen at ranges up to 100 yd; (b) at
ranges beyond 100 yd, a sharp decline in hit probability occurs
and this decline in effectiveness is most marked at the common
battle ranges, between 100 and 300 yd; (c) at 500 yd, both experts
and marksmen perform unsatisfactorily, a performance quite
inconsistent with the design capability of the weapon and with
military specifications.**
These findings provide part of the explanation for most fre-
quent battle use of rifles at ranges less than 300 yd and for the
The author acknowledges the assistance of Lt Col D, E, Munson of ORO in arranging
for these tests and in helping with test designs which were in keeping with the
practical aspects of conditions of combat.
**For the issue M-l rifle and standard M-2 ammunition, the mean radial dispersion is about
ten inches at a range of 500 yd. An indication of the discrepancy existing between the
inherent accuracy of the weapon and ammunition, on the one hand, and that of the man-
rifle combination, on the other, may be found by comparing miss probabilities at the
range of greatest interest, namely 300 yd. In a machine or bench rest, the probability
that the rifle- ammunition combination will miss the type E silhouette target (which
approximates the head and torso region of an erect human target — projected area about
4.6 sq ft) at 300 yd is about PM = .040; whereas, for marksmen firing individually, the
probability of a miss is Pm - 0.76.
16
ORO-T-160
I HIPUMMtm
incurrence of the majority of rifle bullet wounds in combat within
this range. Since deflection errors in aiming are independent of
range (Appendix), the sharp decrease in hits beyond 100 yd is not
to be attributed to men becoming less accurate at the longer ranges
the hit probabilities shown by the curves are a function of target
size and range.
A Experts individually firing new weapon
B Experts firing individually
C Marksmen firing individually
D Marksmen firing simultaneously
Fig. 4 — Marksmanship using the M-l Rifle
(Probability of hitting target as function of range)
The difference between expert riflemen and marksmen,
although significant at some ranges in these tests, may or may
not be meaningful in actual combat where man targets will be in
movement and psychological duress will be high. In fact, in the
rapid fire tests using targets randomly presented (see Appendix,
Test 3), the marksmanship of experts declined significantly when
compared to simultaneous firing in Tests 1 and 2. The same
comparison for marksmen showed that the rapid fire test did not
significantly affect their performance, indicating, perhaps.
ORO-T-160
17
that under the rigorous conditions of combat, only slight differ-
ences exist in marksmanship among the several qualifications as
determined on the range.
In a fire fight, it is reasonably certain that marksmanship
will be less effective than shown by the curves in the tests which,
for this reason, are presumed to be optimistic as relating to the
actual situation.
In connection with the dispersion inherent in the weapon and
in the ammunition used, it is interesting to note that, at all com-
mon ranges, weapon errors are without significance in the man-
weapons system. As already pointed out, considerable discrepancy
exists between the accuracy of the weapon and that of the riflemen.
In the Appendix, it is shown that the -dispersion of the weapon could
be more than doubled without materially affecting the probability
of hitting the target. As shown in Fig. A43, weapons -design
standards which seek perfection by making the rifle more accurate
(approach zero dispersion) would not be reflected in improved
marksmanship or musketry. Such high standards of precision and
accuracy on the part of present designers are not supported by
this analysis as genuine military requirements. Results of
the analysis on marksmanship were also used to predict the value
of using a weapon which would tend to compensate for man-aiming
errors by firing a pattern salvo, or volley.* In Fig. 4, one of
the examples of hit effectiveness for such a weapon is presented
(from the Appendix).
The Pattern Salvo Weapon
As shown by field test, errors in aiming have been found to be
the greatest single factor contributing to the lack of effectiveness
of the man-rifle system. In particular, the men who are graded
by Army standards as expert riflemen do not perform satisfactorily
at common battle ranges, a fact which casts grave doubt on any
The results of the tests on marksmanship already have astonished many persons
because it was not expected that men would exhibit such low performance at the
common ranges. The factors which possibly explain the disparity between the higher
marksmanship scores from Army training methods, when firing on known distance
ranges, and the lower scores from the ORO tests are apparently connected with the
conditions of the tests which neither simulated Army methods of scoring or approached
the true conditions of combat. Perhaps by adopting training methods along the lines of
the tests conducted, the performance of men might show some general improvement. In
any case, the test results are believed to be more indicative of the actual capabilities
of riflemen in a military situation than the qualification score made when firing for
record on the range. The ORO test data already have been used in other analyses
relating to the weapons system and have proven of great value. Because they may prove
useful to other workers in military analysis, the Appendix has been written to include
most of the raw data in the form of tables and figures, resulting in “bulk” for which
there is no other warrant.
ORO -T- 160
g * " 11 11 'SEC RE T
attempt at the development of skills through training which would
begin to approach the accuracy of the weapon itself. Although care-
ful selection and intensive training of personnel in the use of the
rifle may accomplish much in improving marksmanship in peace
time, the problems of rapid Army expansion and accelerated train-
ing in time of national mobilization preclude the opportunity to
develop highly skilled riflemen in large numbers by selection or
through prolonged training. This point is often overlooked by those
who argue for better training as the only solution for the rifle pro-
blem. Actually, to reach truly proficient standards in marksman-
ship, the time required in training would greatly exceed the prac-
tical limits imposed on Army training schedules by the needs of
mobilization.*
In the search for alternatives to an extensive (and impracticable)
training program, consideration was given to the possibility of
compensating for man-aiming errors through a weapon-design
principle. The results of the marksmanship study indicate that a
cyclic or salvo-type automatic fire arm offers promise of increasing
hit effectiveness if the missiles in a burst or salvo were projected
so as to be dispersed randomly or uniformly around the point of
aim. Obviously, a uniform type of dispersion would be more
desirable than random dispersion if hit effectiveness were to be
maximized. In considering such a weapon, two points required
determination: (a) a practical limit on the number of rounds per
burst or volley; and (b) the pattern design of the rounds to be
delivered.
In the Appendix, the consideration of four- and five -round
salvos was not arbitrary. Wound ballistics data show that small
caliber missiles of high velocity could be used in the new weapon
(see section on Wound Ballistics), which suggested the possibility
of obtaining logistic equivalence (that is, equivalence in weight of
weapon and ammunition carried) between a four -round salvo and
present single-shot rifle fire**; also, not less than four rounds
would be required to form a symmetrical pattern (diamond- shaped)
One expert rifleman at Fort Be nning, Georgia , estimated that it required nine years of
continuous training on fire arms to develop marksmanship to the proficient level which
he now enjoys. Sgt. Justice’s performance in demonstrating the use of infantry hand
weapons is most dramatic. His skill in marksmanship actually approaches the accuracy
of the weapon; he has attained a level of performance roughly commensurate with the
design precision of the weapon. However, it is estimated that less than 10 percent of
the men in the normal recruit stream could possibly reach this level of small arms
proficiency, even if time allowed for training were long.
* *
Calculations actually reveal that, for a high velocity, .21 cal missile of 60 grains, the
ratio of cartridge weights for M-l standard ball ammunition and the small caliber rounds
would be about 1.6 : 1.
ORO-T-160 19
around the point of aim which would tend to maximize hit prob-
ability on the human-target shape.*
As shown in the Appendix, a cyclic or salvo-type hand weapon
would materially increase the effectiveness of aimed fire among
the infantry. Although not all possibilities in pattern dispersions
and numbers of rounds were analyzed, it appears that the best
design (for the greatest practical gains) is one using the four-
round salvo with 20 in. spacing among rounds at 300 yd range.
The development of a salvo weapon having these characteristics
represents an ideal toward which effort might be directed; it is
not suggested that this is the only solution.
By considering the need to maintain minimal logistic require-
ments (number of rounds) and minimum weight, a weapon which
conformed to the principle of this design would tend to optimize
the military effects of a fire arm, per se. To add to these gains
materially, an impractical number of rounds per salvo or
burst, or an entirely different weapon would be required**
From the analysis of the dispersion of shots fired at various
ranges, it was possible to calculate the relative effectiveness of
a hypothetical new type, salvo automatic weapon, which was
assumed to differ from the M-l rifle only in the manner in which
the missiles were projected. Examples of the effectiveness of
four- and five-round salvos with 20 in. spacing among rounds at
varying ranges are given in Figs. A41 and A42. It will be noted
that a four-round salvo of 20 in. spacing at 300 yd would more
than double hit effectiveness at this distance. Coincidentally,
this increase, through a design change alone, would raise the
performance of common marksmen using the salvo weapon to the
level of expert riflemen using the M-l.
From this analysis of marksmanship and its relation to a
given weapon, it is concluded that: (a) The marked decrease in
*The analysis (Appendix) suggests that the human target is represented reasonably well
by a circular shaped target. Since the average projected area of the body in combat is
less than 2 sq ft* and a man is about 20 in. wide, the average human target is thus more
nearly represented by a rectangle approximately 12 in. X 20 in. if the profile of the
head on the shoulders were not considered. Considering the head, however, the average
human target in combat does approximate a circle.
A hand weapon could be designed like a Very pistol and project small fragmentation
shells which could be directed at the enemy in much the same way as grenades. By
using the new principle of controlled fragmentation shells and employing some unique
time fuze, it might be possible to reach a level of true maximum effects for fire arms.
The problem would be connected with the fuze and not the launcher if missile bursts
were to be controlled over the heads of the enemy. Such a weapon would require
considerable technical development, involving, probably, a longer range program than
a pattern-dispersion-type fire arm. Any contemplated plan for proceeding with the
development of fragmentation hand arms should cause the dispersion weapon to be an
intermediate step in the developmental chain.
20
ORO-T-160
1
INFORMATION
C
* it* o H
ifey
hit probability occurring between 100 and 300 yd suggests that
significant improvement in effectiveness at these ranges cannot
be achieved by increasing the ballistic accuracy of the weapon:
aiming errors are too great to be compensated by any improve-
ment in the accuracy of the rifle alone, (b) A cyclic or salvo
automatic weapon could compensate largely for these aiming
errors if the missiles were projected with a dispersion pattern
designed to maximize the probability of a hit on the human target
at ranges which most frequently recur in combat (up to 300 yd).
Full -Automatic Fire
The last conclusion prompted an examination of the opera-
tional performance of current models of fully automatic rifles
to determine whether these desirable characteristics obtained.
Two questions were salient: (a) As the fully automatic rifle is
ordinarily aimed and fired, what is the nature of the shot dis-
persion from short bursts? (b) Does automatic fire in short
bursts increase the probability of a hit on a man-size target,
especially at ranges of 100 to 300 yd?
To answer these questions, tests were arranged at Fort
Benning, Georgia, in which both expert riflemen and marksmen
used current models of full automatic rifles. Type E silhouette
targets were mounted in front of six by six-ft target screens.
The first firing serial was at 100 yd using controlled bursts of
five rounds each. Never did more than one round hit the target
or screen from any of the short bursts, and consequently no
information could be obtained at 100 yd on the nature of the
dispersion pattern. To obtain more than one strike on the six
by six-ft screen, the range had to be closed to 50 yd. At this
short range it was noted that the man- silhouette target in front
of the screen was not' hit more than once from any burst. Since
single round firing with the M-l rifle at 50 yd yields a proba-
bility of hit of near unity, the effectiveness of automatic fire
at such short ranges was of no interest.
The results of these trials (although preliminary) strongly
suggested that the emphasis and impetus currently being placed
by the US and other NATO countries on the development of fully
automatic hand weapons should be questioned on the basis of
actual military requirements for the automatic feature. ORO
plans to make further tests* of infantry weapons and some of
these tests will include further work on shot dispersions of
It is planned to :stablif
ORO-T-160
tactical research laboratory at Fort Benning, Georgia.
21
5E'
infantry hand arms. However, any work bearing on the estab-
lishment of military requirements for weapons, especially
automatic hand arms, should provide operational data upon
which decisions can be made. In this connection, it might be
pointed out that the tests on automatic rifles conducted at Fort
Benning, Georgia, do not constitute the type of weapons eval-
uation from which such requirements can be established. In
the reports of these tests, 11 the weakness of automatics from
an operational effectiveness standpoint was not revealed, and
it is unfortunate that such large-scale trials should not have
been designed scientifically to produce data upon which such
facts might be determined. Any comparison of automatic and
semiautomatic weapons should be designed to determine military
effectiveness by relating hit effectiveness with fire power, to
include rate of expenditure.
From the preliminary, yet informative, tests conducted by
ORO on automatic hand arms it may be stated that:
1. Regardless of the skill of the rifleman, only the first
round in a short, fully automatic burst can actually be directed
at a point target.
2. At normal battle ranges, all shots after the first fall off
a man- size target in an approximately linear pattern, the pro-
gressively greater departures* depending in magnitude upon
the characteristics of the weapon and the manner in which it is
held.
3. At all common battle ranges, with present hand-held
automatics, the strike dispersion is so great that moving the
center of impact for the burst to the center of the target would
not increase the number of hits.
4. Even at much reduced ranges, where more than one hit
from a short burst is scored on a man-size target, the use of
a burst can be justified only in a limited sense, since at
these ranges single rounds (semiautomatic) have a probability
of near unity of striking the target. It follows that reducing the
range does not increase the probability of hitting with automatic
fire,** but only of obtaining multiple hits, Moreover, when at
ranges of 50 yd or less, multiple hits become probable, the
*The rifleman, by a more or less difficult compensating effort, may exert a type of
control. Such control is in itself erratic and is not noticeable before 5-10 rounds
have been fired, according to the cyclic rate of the weapon.
*This result is inconsistent with current rifle design, which provides a high rate of fire
in an effort to increase the number of targets hit, as compared with, say, the model 1903
rifle. Thus, automatic fire is not to be justified oil the basis of an increased proba-
bility of obtaining &hit on separated man-size targets.
22
ORCUT-160
ry
f
ire
.903
160
lethality of the burst increases much more slowly than does the
number of hits (see section on lethality).
5. The full automatic feature of current infantry weapons is
valueless from the standpoint of increasing the number of targets
hit when aiming at separated man- size targets.*
Wound Ballistics: Missile Caliber, Mass, and Velocity
Wound ballisticians have recently determined that the "wound-
ing power" or damage capability of a missile is more nearly
proportional to the cube of the velocity than the square. 12 A
reasonable (and acceptable) measure for wound severity is the
maximum volume of the temporary cavity produced in the tissue
by a penetrating missile. It has been found, for example, that
the effect of increasing the velocity of a small caliber missile
more than compensates for the reduced mass. Recent work 11
has shown that, if extreme ranges are not important, a smaller
caliber bullet than the present .30 cal US military standard
might well be used. Moreover, evidence shows that at common
ranges, .22 cal bullets can produce wounds of measurably
greater severity than .30 cal bullets striking with the same
velocity, providing these velocities at target are greater than
a certain critical value.
Although more extensive work will be required in inves-
tigating the effects of nose shape, weight, and other factors as
they affect flight characteristics and wounding ability, it has
been established that smaller bullets can be used to produce
battlefield physiological effects at least equivalent to those of
the present standard .30 cal. Substantial logistics savings would
also accrue from the introduction of substantially lighter and
less expensive cartridges, although actual savings cannot be
expressed quantitatively until further research indicates the
most practical weight and shape of bullet to employ. The areas
of incomplete research should be investigated at the Biophysics
laboratory, the Army Medical Center, Edgewood, Maryland,
where facilities and skilled personnel offer the opportunity to
advance knowledge in this field in a reasonable length of time
and in an important way.
*
During the course of this study, the author considered the various possible uses of
present automatics in combat where the automatic feature (and the wide dispersion of
rounds) would be militarily useful. Discussion with experienced infantry combat
commanders and other military specialists led to the conclusion that although the
feature was useful in tight, close-in positions, usually another weapon (e.g., a grenade)
could be used to greater advantage than could a burst from an automatic. Also, it was
indicated that, for the average rifleman, such occasions were rare and did not consti-
tute a basis for justifying the feature.
ORO-T-160
Quite apart from the idealized concept of a salvo weapon,
sufficient evidence is at hand to be quite certain that a light,
high-velocity, small caliber rifle could be designed for military
use and could fulfill effectively the role of a general purpose,
lightweight hand arm.
In a recent study 14 conducted by D.L. Hall of the Terminal
Ballistics Laboratory, Aberdeen Proving Ground, a theoretical
comparison of the effects and military usefulness of various
calibers of rifles shows that, when the combined weight of wea-
pon and ammunition is held constant to 15 lb, the over-all
expected number of kills for the .21 cal rifle is approximately
2.5 times that of the present standard .30 cal rifle. When
compared to M-l ammunition, a .21 cal missile of high velocity
(about 3500 feet per second muzzle velocity) creates equal or
greater damage than the standard .30 cal missiles at ranges
up to 800 yd. This evidence, combined with the work of Proj-
ect BALANCE (ORO) on ranges of visibility, marksmanship,
and actual operational needs, lends considerable support to
the major conclusion that lighter hand weapons of smaller
caliber may well be provided without losing military effec-
tiveness, while offering both impressive logistical gains and
improved operations.
In addition to these gains, the advantages of low -recoil
effects offered by the smaller caliber weapons would be reflected
in improved skill in the use of the weapon by allowing a higher
rate of single -round aimed fire. Such weapons would also be
much less fatiguing to handle. Since recoil of a small caliber
weapon would be less than that of present weapons, the disper-
sion of rounds in a short, fully automatic, burst could be
considerably less than the dispersion of current models. This
important characteristic, yet to be determined by actual trial
of small caliber automatics, might possibly be the most prac-
tical solution to the problem of developing an automatic fire
arm which will project missiles in a burst such that the dis-
persion of rounds, at ranges up to 300 yd, would approach the
ideal dispersion for maximum effects as indicated in the
Appendix.
The studies and experimental development work* currently
being undertaken by the Ordnance Corps at Aberdeen Proving
Discussion with G. A. Gufstafson of the Small Arms Section of BRL indicated that it is
feasible to design small caliber, high velocity, automatic rifles, which would exhibit
short-burst dispersion patterns at ranges up to 300 yd, tending to approach
dimensionally the ideal patterns outlined in the Appendix.
24
ORO-T-160
SB
LATION
PWTORMATION
1 !
U
\
I * \
&ddlifo
Ground should be encouraged to proceed toward a rifle develop-
ment which will fulfill these important military characteristics.
Although such a light weapon would not compensate for human
aiming errors when fired semiautomatically, it is quite possible
that automatic fire in short bursts at common battle ranges
would produce dispersion patterns commensurate with the
requirements of the idealized salvo weapon. In particular, the
low recoil of a small caliber rifle offers the chance to employ
a muzzle compensator with significant effects, lending added
promise to a satisfactory development. If the development of
this light, high velocity weapon could proceed to include the
ideal salvo principle, obviously a truly effective hand arm
could be provided.
LETHALITY
Weapons in General
The history of the development of weapons and tactics shows
an interesting process of self -adjustment. It has been found,
from an examination of many campaigns from Marathon to
Korea, that battles are no more bloody now, despite vastly
"improved" weapons, than they were in the days of the short
sword: the casualties incurred per number of men
engaged per unit of time remains about constant.* In fact,
it may well be that the sword is much more lethal than con-
ventional weapons because it can be directed with more
control at the vulnerable areas.lt remains to be seen whether the
tactical use of atomic and new CBR weapons will alter this
trend.
The explanation for this apparent constancy in the intensity
of battle effects seems to be related to the compensating
changes in tactics which each new weapon introduces. Most
advances in weapons either increase the distance over which
a blow can be delivered (improved launcher) or increase the
lethal radius or radius of effect (improved missile), or both.
The ratio of the lethal area to the concentration (or density)
of enemy targets appears to have remained constant. Since
logistics costs have markedly increased since the early wars,
war itself has become vastly more costly in terms of the
effect-cost ratio, yet little if any more effective in terms of
personnel casualties per unit time or per unit effort.
From an unpublished ORO study.
| W' '
f A f Q l t * ir * o. a
ION
ORO-T-160
25
Although these are measures of gross intensity for war
(total casualties only), it is interesting to note that severity
of weapons as measured by their lethality has not changed,
at least in the past century. If the lethal indices of weapons
(also a constant) could be raised, efficiency and effect might
well be improved materially, and no compensating tactical
adjustment would be practicable. It is believed that the
means for doing this are at hand, and, with special reference
to one weapon (the infantry hand arm), an estimate is made
in a following section of expected results if bullet lethality
were increased, as seems technologically feasible.
The Rifle
The lethal index of a weapon corresponds roughly with
tactical effectiveness since it refers to those wounds which
are speedily lethal, the condition of which cannot be reversed
by medical intervention. Since, by this definition, "lethal 1 '
effects result in death very quickly (or death is assured),
the lethal index is a measure of tactical effect. Therefore,
in the forward areas of the combat zone, where bitter hand-
to-hand fighting occurs, there is no sound basis for arguing
against the merit of disposing of the enemy in the shortest
possible time by inflicting maximum physical trauma. For
the infantry hand arm, the infliction of severe wouifds, that
are immediately incapacitating, is important.
As stated earlier, the lethal index of the rifle exceeds
30 percent when hits at all ranges are considered, and,
with the exception of the machine gun, it is the most lethal
weapon of all conventional missile projecting ground arms.
Comparison of Lethality of an
Ideal Dispersion Automatic with M- 1 Single -Shot Fire
From Table A9 and Fig. A40 in the Appendix, it is pos-
sible to estimate the lethality of an ideal dispersion weapon
at the various battle ranges and compare these effects with
those of the rifle. Because no exact information exists
concerning the vital area complex of the body or the effects
on lethality of multiple hits, it was necessary to assume that
all bullets from a salvo, or burst, are independently lethal
and that multiple hits are incurred at random relative to the
vulnerable areas. Obviously, this assumption ignores the
fact that physiological effects of multiple wounds are cumu-
lative (shock, exsanguination, and the like), and that hits
26
ORO -T -160
e
1
4
^ if*' o
Ifjj i j • J
from the ideal dispersion weapon follow a pattern design and
do not, therefore, strike at random. Since cumulative effects
of multiple wounds add to lethality, and since any lack of
randomness in the hits may or may not favor the probability
of striking mortally vulnerable areas, the estimates given may
be strengthened perhaps by the compensating effects of these
two indeterminate factors. For each weapon, is assumed
that the lethal probability of a bullet hit is O.3.*
From Table A9 (Appendix]^ the lethality for the dispersion
weapon (five -round salvo pattern) can be estimated for each
category of single and multiple hits for each range. An
example of the method used is given for a range 200 yd:
Probability of kill per bullet hit, PI = 0.3;
Probability of not killing per hit, Ps = 0.7.
Thus, for each category of possible hits from a five-round salvo:
Hits
Ps
PI
1
0.700
0.300
2
0.490
0.510
3
0.343
0.657
4
0.240
0.760
5
0.168
0.832
For range 200 yd (Table A9), the probabilities of obtaining
exactly 1, 2, 3, 4, and 5 hits with the five -shot patterns are:
Hits
1
2
3
4
5
Ph**
0.388
0.122
0.284
0.0580
0.000
therefore,
PhxPl = 0.116 0.0622 0.187 0.0441 0.000
At range 200 yd, the probability of killing an enemy per
burst is the sum of the lethal probabilities = 0.409.
For single rounds from the M-l rifle at 200 yd, the kill
probability is 0.135 (Ph = 0.45 and PL = 0.3, Fig. A40). In
The lethal index of the rifle bullet exceeds 30 percent. It is assumed that the smaller
caliber bullet for the new weapon would be equally lethal since it will have a wounding
capability equal to or greater than the M-l at the ranges involved.
The variations noted in the probabilities for obtaining more than one hit are due to the
shape of the human target as it affects a strike of two or more hits from the dispersion
pattern.
f fnnfn
_ «
(J 1 [LI H
1 i |
* K + t
-160
ORO-T-160
27
TION
this way, the lethality of the two weapons may be compared
as shown in Fig. 5.
The curves giving the lowest lethal limit* and the prob-
able upper limit for the dispersion weapon show that a
considerable relative increase in lethality over the rifle may
be expected through the use of the dispersion weapon for
ranges beyond 100 yd. The theoretical upper limit would
x
H-
LU
_J
LL
O
>-
CD
<
CD
O
a:
Q.
RANGE (YD)
Fig. 5 Comparison of lethality per aimed shot or burst for the M-l Rifle and
the Salvo Automatic.
exceed the M-l rifle by about a factor of three, if the basic
assumptions used in the estimates can be accepted as rea-
sonably valid. Obviously, at ranges less than 100 yd, the
dispersion of the rounds in the salvo pattern becomes greatly
diminished as range is decreased. Consequently, the lethal
effects will not differ greatly from the single -round rifle
especially when zero range is approached. This variation
in pattern size with range points up the difficulty of attempt-
ing to assess comparative lethal effects at the shorter ranges
and also reveals the weakness of the estimates at the greater
distances.
IMATION *
Quite apart from any consideration of or comment upon,
the protocols and conventions according to which the rules of
land warfare have been codified, it is proper to estimate in
a purely physical way the results of the use of toxic missiles
in such weapons.
Consequently, Fig. 5, the two weapons have been com-
pared for a use of toxic missiles.* It is interesting to note
that, by the addition of toxic missiles to the M-l rifle, the
lethal effects thus produced are about equivalent to the
theoretical upper limit on physical effects given for the dis-
persion weapon. On the other hand, the employment of toxic
missiles in the dispersion weapon offers, in toto, still greater
gains; such effects would constitute an order of lethality not
achieved by any missile projecting ground weapon yet devised.
Can Lethality Be Increased?
The lethal indices of present weapons cannot be improved
materially (if at all) by increasing the effective "hitting power"
alone, since the mortally vulnerable regions of the body set
a limit to the gain. However, by combining chemical toxi-
cants with physical missiles, it is possible to make the entire
body vulnerable by utilizing the circulatory system as, in
effect, a "missile track" which produces certain lethal effects.
Rather than 30 percent fatalities derived from bullet hits, this
procedure would cause the body to become mortally vulnerable
to virtually all of the hits received. Quite apart from the
relative increase in lethality brought about by the design of a
dispersion weapon as shown in the preceding section, the
following analysis on toxic missiles has been included to show
the nature of the relative gains to be expected in the dispersion
weapon if toxicants were introduced in future warfare. The
gains to be described are purely speculative and would provide
additional gains only to the physical lethality of the dispersion
weapon. Although not a necessary adjunct, should toxicants
be employed, the smaller missiles suggested for the new wea-
pon would be more efficient vehicles of the agent than the
larger .30 cal bullets.
Developmental work in the field of toxic missiles is rea-
sonably complete and shows that up to 90 percent of hits from
agent-loaded bullets at common ranges may be expected to
*As indicated later, a lethal probability P = 0.9 was assigned to each toxic loaded
round. The curves were established by taking the product of the probability of a hit
and the probability of lethality for toxic missiles. (See Table A9 and Fig. A40.)
f f
l I ^
-160
ORO-T-160
29
nplq nr*
incapacitate in a matter of minutes and bring about death
regardless of the region of the body struck. 15 The agent
used is stable (in storage, it is as stable as any other part
of the round); it can be manufactured in large supply at low
cost; its toxicity is about as high as any substance known.
The physiological effects produced by the agent are similar
to the G- agents: death is rapid and the course of the effects
is violent. The progress of the physiological symptoms is
demoralizing to witness; thus real psychological effects not
normally characteristic of weapons design are added.*
Since it has been found that small missiles (such as .22
cal) are more efficient vehicles for such toxic agents than are
the larger calibers/ 5 the application of toxic missiles to a
small caliber hand weapon as herein proposed is particularly
adaptable. To the increase in hit effectiveness brought about
by the use of the dispersion weapon, an impressive gain in
the lethality of these hits might be added. Thus would be
achieved a genuine innovation in a weapons system which has
exhibited through history a constancy in lethal effects.**
Data from the last two World Wars show that for ground troops
the ratio of killed to wounded (all ground weapons) was, for both
periods, about 1:4.1. About 20 percent, then, are killed in action. 1
With the single addition of toxic bullets for small arms to the
whole weapons system, the ratio of KIA to WIA in these past two
wars would have been raised from 1:4.1 to about 1:2.1, or, on
the average, the lethal index of all weapons would have increased
12 percent, from 20 percent to 32 percent.***
Although these figures are crude estimates of the gross
or over -all gain which might be expected by the employment
of toxic missiles, it is probable that the gain would be a
Apart from flaming weapons, ordnance development has not taken advantage of possible
designs to produce fear in the enemy as well as physical damage. Toxic missiles do
offer the possibility of combining the elements of physical and psychological trauma for
maximum effects. [See also ORO-B-3, Appendix H, (SECRET)]
Against toxic missiles, certain defense measures could be adopted. A suitable antidote
could be carried by each man in the form of an ampule and injection could be performed
through the clothing using the same methods as planned for defense of G-agent
poisoning. Also, if small caliber missiles were used and the bullets were designed to
encourage rapid disintegration in the wound track, light (plastic) armor might be used.
In both of these areas of defense, the Soviet may be weaker than the US in the initial
phases of toxic missile employment but it is certain that, like all other technical
advantages in warfare, a process of neutralization will occur whereby neither side has a
material advantage because of the equalizing effects of the defense measures which
both sides eventually adopt. Furthermore, speedy retaliation in kind should not be
difficult for either side.
Enemy reactions must be anticipated.
30
™>^ - I
ORO-T-160
*
SEO
NATION
strategic one rather than tactical* In an ORO analysis of
battle casualties as to their period of non-effectiveness, 16
data indicate that ideal toxic missiles would do little further
to reduce enemy strength during any battle situation but may
exert considerable influence over an extended campaign.
Finally, it must be remembered that only by improving the
hit capability of the weapon, as herein proposed in the dis-
persion weapon, would one expect maximum gains in the
tactical situation if toxic missiles were introduced.
THE DISPERSION WEAPON
Basis of Issue (T/OkE)
It is to be emphatically stated that the new type hand arm,
as proposed in this study, should not entirely replace the longer -
range rifle in the unit organization. In most tactical situations
there is a definite requirement for sniper (highly specialized)
fire. It is also important to maintain a degree of versatility
responsive to the dynamic tactical situation. Consequently, it
is believed that the precision-aimed, long-range rifle must be
retained for that limited but existing employment which its
design characteristics actually fit. Limited knowledge of sniper
fire indicates that at squad level it is not employed frequently
in the fire fight but has an important role in the defense or in the
less fluid conditions (maneuvering for build-up, and so forth)
preceding a hot action* As far as can be determined by ques-
tioning combatants, the ranges of sniper fire are mostly within
the tactical damage range of the small caliber, high velocity
missiles (i, e. , up to 800 yd). This suggests the possibility of
using weapons of the same caliber as the general purpose hand
arm, but designed for precision, long-range use. However,
the whole question of sniper fire in battle is yet to be analyzed
from an operations point of view; until this is done little can be
said concerning weapons requirements for specialists in this role*
About 20 percent of the total hits of these past wars have been bullet hits. Of those hil
roughly 30 percent are KIA. (On limited knowledge of enemy Japanese rifles of WW XT.)
Thus, toxic bullets would result in 90 percent KIA among those hit and increase the
lethality of the bullet by a factor of 3*. Thus the total killed by bullets would increase
from, 20 X 0.3 — 6 percent to 20 X 0.9 = 18 percent. The total killed (all weapons)
would then increase from 20 percent to 32 percent of those hit, (Note: The figure, 6
percent, for fatal bullet hits may be low for small arms fire; Tribby’s analysis of 1,000
KIA in the ETO attributed about 11 percent of those killed to small arms fire.)
ORO-T-160
31
SECUR
* IP* 3
\ &
\ ? ^ ^ ? t,7m
The question of< a general purpose hand arm is not one of
supplanting a long-range precision arm, but rather of replacing
a certain number with a different weapon, each type having its
own proper and effective tactical application.
It is believed that a practical and useful beginning can be
made in deciding upon the optimum ratio of short-range hand
arms to long-range precision rifles by noting the figures for
ranges of engagement which have been presented earlier. On
the average, it has been found that 70 percent of the ranges over
which a man-size target is visible to a defending rifleman lie
within 300 yd. Since the short-range weapon will be designed
according to specifications for maximum effect up to 300 yd,
it may be suggested that 7 in every 10 infantry hand weapons
should have the characteristics desirable for short-range use.
Although this target- visibility criterion, employed to set an
upper limit to the range of engagement, ignores certain vari-
ables within the small infantry unit which bear on control and
communications as well as many of the problems of musketry
and maneuver, it may be received as a tentative and preliminary
basis for issue.
Another approach to the determination of an optimum ratio
for hand weapons is to consider the aptitudes of enlisted men
normally received from the manpower pool. From experience
at Fort Benning;* the development of no more than two expert
riflemen per squad may be expected from the normal recruit
stream without special training. Unless present training sched-
ules and methods are altered to permit improvement in marks-
manship skill, this tends to set an upper limit on the number of
highly skilled riflemen that it is feasible to assign to the squad
from the standpoint of natural aptitudes available to the Army,
and of the training effort.
The figure(two experts per squad) is consistent, however.
This does not mean that it would not be desirable to have much
higher performance in marksmanship among all the men in the
squad; the suggested assignments for experts merely empha-
size the operational need for at least two experts per squad if
training is unavailing in raising present standards of performance.
It was not possible to obtain data from the AGO, "G-3, or OCAFF on the number of
enlisted men who could be expected on the average to pass as experts. In private
communication with Fort Benning, the Infantry School has indicated that about 10
percent of the men receiving marksmanship training could be expected to pass as
experts by known distance range firing standards.
with that already given as the apparent actual requirement.
32
ORO-T-160
To arrive with assurance at an optimum ratio, much more
knowledge of small unit operations in combat would be required
than is now known in ORO or elsewhere. Determinations at a
"tactical laboratory, " such as ORO is eager to see established
at Fort Benning, could contribute much to the solutions.
Training
The increases in effectiveness which have been proposed in
this analysis all follow from innovations in design of the weapon
for the purpose of overcoming deficiencies ip skill or training
and for adapting the weapon to the nature of its actual opera-
tional employment. Since there ia no reason to suppose that
the new weapon would be char act eric ally unlike the present
rifle in its method of operation, no increased demands for train-
ing time or facilities are visualized. In fact, the short range
of the weapon offers a chance for considerable reduction in
weight and for less precision in working parts. Consequently,
development of a lighter weapon, with low recoil, should facil-
itate training in its use.
Also, it is felt that men would react favorably to a weapon
which increased their own marksmanship performance since
it would add to their confidence in being able to hit the enemy
at ranges where M-l rifle fire is comparatively ineffective.
It does not seem reasonable to assume that a man's confidence
in his weapon would be affected adversely by a design which
increased his chances of hitting the enemy and therefore in-
creased the probability of his own survival.
In connection with present marksmanship training, the results
given in the Appendix suggest strongly that considerable improve-
ments are needed if skills are to approximate the precision capa-
bilities of the M-l rifle. An examination of the current basic
training program shows that 76 hours are allowed for marksman-
ship training with the rifle, of which only 48 hours are involved
in "wet" exercises, that is, actual range firing of the weapon. 17
In the 48 hours of training, each man fires at least 400 rounds,
which indicates roughly the total amount of time spent in the
actual employment of the rifle. Any question of the adequacy of
this training program could only be settled by field tests designed
to determine the best methods and the time required to produce
optimum results among men in their marksmanship skills. As
shown in the Appendix, it is not likely that training alone could
be effective in materially raising the standards of all men to
exceed the level of expert performance indicated by the Belvoir
ORO-T-160
33
tests. Significant gains in man -weapon effectiveness are to be
obtained only by combining improvements in weapon design with
good training. By the adoption of design principles in a hand
weapon, as proposed in this study, an opportunity is offered to
realize gains of considerable magnitude.
Design Feasibility
No insoluble problems appear to be involved in the engineering
of a weapon possessing the recommended characteristics. To
accomplish ideal dispersion in an automatic hand arm , as ideal-
ized in the Appendix, many design difficulties will stand in the
way of preserving desirable military characteristics such as
lightweight, durability, reliability, automatic loading, and
other factors. A salvo-type automatic which projected volleys
of rounds to form the desired pattern at the range giving maximum
hit effectiveness probably would represent the best type of design
for deriving the greatest gains. This would entail designs which
include the multi -barrel principle, high cyclic rate single-barrel
types with a design feature for allowing the barrel to nutate at
the muzzle on recoil for controlled dispersion, frangible missiles,
aer ©dynamically controlled missiles, compensators, deflectors,
and the like, all of which present a variety of engineering diffi-
culties to be overcome before the weapon would function satis-
factorily, The point of chief concern, however, is to strive for
the attainment of the pattern dispersion principle so that the
greatest possible gains can be derived, and in the striving, let
the engineering difficulties argue for themselves.
In studying the design problems, it was apparent that the
smaller caliber weapon, with its bullets of smaller mass, would
have considerably less recoil than present automatics, and that
the reduced dispersion of a burst, along with the employment of
a muzzle compensator, should have significant effects in reducing
muzzle 11 walk -off. " As stated previously, it may well be that a
light automatic of small caliber (in the region of .20 cal) would
produce dispersions of rounds in short bursts which are not
incongruous with the pattern dispersions specified in the Appendix.
At least the tendency would be a significant reduction in dis-
persion as compared to present automatics with their high recoil
effects. Such reduction may be sufficient to regard the dis-
persion as approaching the optimum requirements.
Considering all factors, this approach to the problem appears
to be straightforward, practical, and relatively simple, and it
offers promise of fulfilling the desirable optimum dispersions
£ :
34
ORO-T-160
for maximum hit effectiveness. Tests on prototype models of
new weapons of small caliber should be made to determine the
practicality of this approach to the problem.
A THEORY FOR DETERMINING
RELATIVE EFFECTIVENESS OF DIRECT FIRE WEAPONS
The analysis would not be complete if advantage were not
taken of possible valuable theoretical applications which may
be made using the two major parameters given in the analysis
of the man-rifle system. These parameters relate to the prob-
ability of seeing a man target on the battlefield and the probability
of hitting the target with aimed fire.
To test an hypothesis, according to which effectiveness might be
evaluated, use was made of battlefield visibility data for the area
of Korea where ranges were known for a small sample of rifle
bullet hits among members of the Turkish Brigade.
Method Used
The method which has been used in estimating the expected
distribution of hits as a function of range may be open to serious
question because of the possible weakness of the assumptions
made about actual rifle operations. Although the need was recog-
nized for more adequate knowledge of the factors which exert a
major influence on aimed rifle fire, it was felt that the data on
visibility and hit probability might be useful for computing the
expected distribution of hits as a function of range for different
weapons. As shown in Table 1, the probability product of the
hit data and of the visibility data for each range interval yields
predictions on the relative distribution of hits, if one assumes
expenditure proportional to targets seen and targets seen pro-
portional to the map measurements on visibility.
In Table 1, the data given for Ps are the fraction of all
cases where a man can be seen continuously in the 50-yd inter-
val. Employment of the data sets up a model which visualizes
the enemy approaching a defender who fires on the enemy when
he first appears. The results of the repetition of many cases
of this simple dual situation should permit prediction of the
type of distribution of hits as a function of range, for aimed rifle
fire over the Korean terrain. While it is possible to calculate
the number of hits to be expected as a function of range using
column 4 of th er of hits cannot be
ORO-T-160
35
: ORMATlON
8 $
f >
isV-Mi*
I ^
r -rS-f'i |
, ...... *.viUuOL. ww . ,
compared with the observed number because the sample of
combat data did not provide information on the total number of
men involved or the expenditure of rifle ammunition. For this
reason, the percentage distribution of expected hits was com-
pared to the observed distribution.
TABLE 1
COMPUTED DISTRIBUTION OF HITS AS FUNCTION OF RANGE R
Range
Interval, yd
Ps a
Ph b
Ps x Ph
Ps x Ph,
Normalized
Accumulated
“Expected
Fraction
of Hits”
0-49
0.360
1.00
0.360
0.457
1.000
50-99
0.254
0.93
0.234
0.297
0.543
100-149
0.162
0.76
0.123
0.156
0.246
150-199
0.070
0.54
0.037
0.047
0.090
200-249
0.047
0.38
0.018
0.023
0.043
250-299
0.028
0.28
0.008
0.010
0.020
300-349
0.024
0.22
0.005
0.006
0.010
350-399
0.016
0.17
0.003
0.004
0.004
Totals
0.788
1.000
^Probability of seeing target within each interval.
Probability of hit-
In Fig. 6, the distribution for the calculated fraction of hits
corresponds roughly with the distribution of actual hits in com-
bat in Korea.
As a matter of interest, the M-l rifle and the five-round
salvo type weapon were compared in this way for the two extreme
types of terrain, Class A and Class C. The expected distribution
for hits from both weapons at ranges greater than R for the
Korean terrain and for the Normandy terrain is given in Fig. 7.
Since these distributions do not show the relative effectiveness
of the two weapons, the same model was used to provide an
indication of the merits of the salvo weapon over the rifle as
terrain influences effectiveness.
In this instance, as shown in Table 2, the hits were calculated
on the basis of 100 shots fired for each weapon at man targets
distributed over terrain in accordance with the distribution given
for Ps.
36
ORO-T-160
5ECURI
'ION
PROBABILITY OR FRACTION
r
0 100 200 300 400 500
R- RANGE (YD)
Fig. 6 — Rifle marksmanship, battlefield visibility, and hit probability in
combat. A: Ph, probability of hitting man-target as function of range;
B, observed fraction of hits occur ing at ranges greater than R; C, proba-
bility of seeing target at ranges greater than R(l-Ps); D, computed frac-
tion of hits expected to occur at ranges greater than R(Ps x Ph, where
Ps is converted to frequency of visible areas occuring in each 50 yd
interval, and where Ph is averaged in each interval by assuming the
mean P value).
* Assumes expenditure proportional to targets seen and targets seen proportional
to Ps.
ORO-T-160
m
INFORM?
SECURITY
HIT PROBABILITY
s ulum i i u t m r mmmmm
A
t yrt, r* J fy f* - 1
j> f 1
Fig. 7 — Theoretical distribution of hits as function of range for M-l Rifle and a Salvo-
Type Hand Weapon for Class "A” and *‘C” Terrains.
TABLE 2
RELATIVE EFFECTS OF M-l SINGLE-ROUND FIRE AND SALVO FIRE
AS FUNCTION OF RANGE FOR TERRAIN TYPES A AND C
Range
Interval* yd
Ps a
Ph b
Expected Hits
Ps x Ph,
Normalized
Class A
Class C
M-l
Salvo
M-l
Glass A
Salvo
Class A
M-l
Class C
Salvo
Class C
0-49
0.360
0.05
1.00
1.00
37
37
9
9
50-99
0,254
0.10
0.93
0.99
24
26.
16
17
100-149
0.162
0.09
0.76
0.96
12
16
12
15
150-199
0.070
0.09
0.54
0.89
4
6
8
14
200-249
0.047
0.09
0.38
0.81
2
4
6
12
250-299
0.028
0.06
0.28
0.71
1
2
3
9
300-349
0.024
0.06
0.22
0.60
1
1
2
6
350-399
0.016
0.04
0.17
0,49
0
1
_1
3
Totals
0.961
0.58
81
93
57
85
^Probability of seeing target within each interval
■'probability of hit.
38
assiti
mm mm
ORO-T-160
100
100
80 — N
\
\
\
\
\
CLASS C TERRAIN
(Normandy)
0
100
200
300
400
0
100
200
300
400
RANGE (YD)
Fig. 8 — Relative effectiveness of M-l Rifle and Salvo Automatic for Class "A" and
"C” Terrains.
It will be noted in Fig. 8 that the comparative effectiveness
of the salvo weapon is much greater for open terrain types like
Class C than for terrain types of Class A because of the greater
hit effectiveness of the salvo weapon at the longer ranges. Such
information, although only relative, suggests that the dispersion
type hand weapon would offer material advantages over the M-l
rifle in areas of combat such as western Europe. On the other
hand, the advantages of the new weapon in areas like Korea are
not as great and the comparison made in Fig. 8 supports the
contention that a hand weapon designed for semiautomatic use
in the short ranges and for full automatic use in the longer
ranges with controlled dispersion would offer a good solution
for the common hand arm.
If theory, as herein presented, can be confirmed by more
extensive knowledge of expenditure and ranges of hits incurred
in combat by the rifle and other direct fire weapons to include
machine guns, recoilless rifles, antitank weapons, and the
like, the method would constitute a promising basis for eval-
uating a balanced weapons system, and T/O&E for units might
be established on a quantitative basis.
ORO-T-160
39
f, ? r*- -
CONCLUSIONS
1. The ranges at which the rifle is used most frequently in
battle and the ranges within which the greater fraction of man
targets can be seen on the battlefield do not exceed 300 yd.
2. Within these important battle ranges, the marksmanship
of even expert riflemen is satisfactory in meeting actual battle
requirements only up to 100 yd; beyond 100 yd, marksmanship
declines sharply, reaching a low order at 300 yd.
3. To improve hit effectiveness at the ranges not covered
satisfactorily in this sense by men using the M-l (100 to 300
yd), the adoption of a pattern-dispersion principle in the hand
weapon could partly compensate for human aiming errors and
thereby significantly increase the hits at ranges up to 300 yd.
4. Current models of fully automatic hand weapons afford
neither these desirable characteristics nor adequate alternatives.
Such weapons are valueless from the standpoint of increasing
the number of targets hit when aiming on separated man- size
targets.
5. Certain of the costly high standards of accuracy observed
in the manufacture of current rifles and ammunition can be relaxed
without significant losses in over-all hit effectiveness.
6. To meet the actual operational requirements of a general
purpose infantry hand weapon many possibilities are open for
designs which will give desirable dispersion patterns (and accom-
panying increases in hit probability) at the ranges of interest. Of
the. possible salvo or volley automatic designs, the small caliber,
lightweight weapon with controlled dispersion characteristics
appears to be a promising approach. (Low recoil of a small cal-
iber weapon facilitates dispersion control. )
7. To create militarily acceptable wound damage at common
battle ranges, missiles of smaller caliber than the present stand-
ard .30 caliber can be used without loss in wounding effects and
with substantial logistical and over -all military gains.
8. A very great increase in hit lethality can be effected by
the addition of toxic agents to bullet missiles.
RECOMMENDATIONS
1. It is recommended that the Ordnance Corps proceed to
determine the design or technological feasibility of developing a
ORO-T-160
>N
f j 3 ft ^ i s ** 1 1 1 *h : i i
w i iv3 wty wiliiry
hand weapon which has the characteristics cited in this analysis*
namely:
a. Maximum hit effectiveness against man targets within
300 yd range. (This does not mean that the weapon will be ineffec-
tive beyond this range. )
b. Small caliber (less than .30).
c. Wounding capability up to 300 yd at least equivalent to
the present rifle.
d. Dispersion of rounds from salvos or bursts controlled
so as to form a pattern such that aiming errors up to 300 yd will
be partly compensated, and hit effectiveness thereby increased
for these ranges.
2. As one possible alternative to the current "volume of fire"
(fully automatic) approach to the problem of increasing the effec-
tive firepower of infantry riflemen, it is recommended— subject
to tentative confirmation of design feasibility— that a rifle incor-
porating at least in principle the military characteristics here
proposed be manufactured for further and conclusive test.
ORO-T-160
41
lATION
BIBLIOGRAPHY
1. Gardner, John H. ; Hitchman, Norman A.; Best, Robert J,
ORO-R-5: ALCLAD Final Report, Appendix A.
1 August 1951 (SECRET).
2. Johnson, Ellis A.; Parker, Edward M.; and ORO Staff.
ORO-R-3: MAID Report , Appendix H.
21 January 1950 (SECRET).
3. ORO-R-5, Appendix B (SECRET).
4. DeBakey, M. and Beebe, G. Battle Casualties. Springfield,
Illinois: C. Thomas Co., 1951 (UNCLASSIFIED).
5. Oughterson, Col. A. W. Wound Ballistics Report ,
Bougainville Campaign, 1944 (RESTRICTED).
6. Office of the Surgeon General, Wound Ballistics Survey ,
Korea (15 November, 1950-5 May 1951) (CONFIDENTIAL).
7. AORG liaison Letter, December 1951 (SECRET).
8. Donovan, Grace N. ORO-T- 18{FEC): Use of Infantry Weapons
and Equipment in Korea . August 1952 (SECRET).
9. Kaye, J. D. The Use of Infantry Weapons in Korea .
ORS/Korea. Report No. 6, 12 March 1952 (SECRET).
10. Bayly Pike, D. F. and Goepel, Charles. ORO-T-161: The
Effects of Terrain on Battlefield Visibility (SECRET).
11. Army Field Forces. Report of Board No. 3, Project 2231 ,
Vols. I and II. Fort Benning, Georgia, 27 October 1950
(SECRET).
12. National Research Council. Missile Casualty Reports ,
Nos: 1 to 17.
13. Chemical Corps Medical Laboratory, Wound Ballistics of
a .22 Caliber Brass Scale Model of the .30 Caliber M-2
Rifle Ball , Research Report No. 94, December 1951
(CONFIDENTIAL).
14. Hall, D. L. An Effectiveness Study of the Infantry Rifle ,
BRLM 593, March 1952 (CONFIDENTIAL).
15. Army Chemical Center. Reports on Project 4-04-19-001
(SECRET).
16. ORO unpublished Study.
17. FM-23-5, US Rifle Cal .30 M-l, October 1951 (UNCLASSIFIED).
42
ORO-T-160
sisuKT^5Erin!^®®^fr oN
f
i
APPENDIX
ANALYSIS AND APPLICATION OF
RESULTS OF RIFLE-RANGE TESTS
V
IN
? £% i
i iUi
APPENDIX
ANALYSIS AND APPLICATION
OF RESULTS OF RIFLE-RANGE TESTS
CONTENTS
Page
SUMMARY
49
INTRODUCTION
49
ANALYSIS
50
Objective — Data from Tests — Determination of
Means (mpi) and Dispersion (Standard Deviation) —
Summary of Means and Standard Deviation — Disper-
sion as a Function of Range — Systematic Errors in
the mpi — Comparison of Observed and Theoretical
Distributions of Deviations from mpi — Remarks on
the Homogeneity of Results for Individual Riflemen —
Remarks on Deviations of mpi from Aiming Point —
Comparison of Observed and Theoretical Probabilities
of Hitting Target at Various Ranges — Remarks on
Results of Firing on Targets Appearing Randomly at
Either of Two Ranges.
APPLICATION 91
Theoretical Probability of Hitting Type E Silhouette
Target With a Salvo Pattern — Probabilities for 1,2,
3,4, and 5 Hits on Man-Size Target With Five-Shot
Pattern Salvo — Comparison of Theoretical Probabil-
ities of Hitting “Average Target" with Single -Shot
and Five-Shot Pattern Salvo — Remarks on Significance
of Probabilities of Hitting a Target with a Single-Shot
and with Five-Shot, Four -Shot Pattern Salvos — Effect
ORO-T-160 45
IN
Page
^rvPI
t >
1 it* on
CONTENTS (Continued)
of Weapon Dispersion on Probability of Hitting
Target.
FIGURES
A1-A32. Shot Patterns on Target and Screen, Tests
1 and 2.
A33. Example illustrating use of probability paper
to determine standard deviations and means,
whether or not distribution is truncated
A34. Observed standard deviation, S r , of distance
of individual shots from mpi as function of
target range, for experts
A35. Observed standard deviation, S r , of distance
of individual shots from mpi as function of
target range, for marksmen
A36. Distance of mpi from top of target as function
of range
A37. Distance of mpi from vertical line through
target center as function of range; Test 1
A38. Distance of mpi from vertical line through
target center as function of range; Test 2
A39. Probability of expert riflemen hitting Type E
silhouette of range
A40. Probability of marksmen hitting Type E silhou-
ette target as a function of range
A41. Probability of hitting Type E silhouette target
with single shot compared with probability of at
least one hit with a five -shot pattern salvo;
curves based on aiming errors
ORO-
75
76
78
80
84
85
86
88
89
92
-160
Imation
FIGURES
CONTENTS (Continued)
Pag
A42.
Probability of hitting “average" target. A,
with single shot compared with probability
of at least one hit on target with five-shot
pattern salvos.
94
A43.
Probability of hitting a circular target as
function of range for several weapon-ammu-
nition errors
97
TABLES
AI.
Rifle Range Test 1
98
A2.
Rifle Range Test 2
99
A3.
Rifle Range Test 3
100
A4-5.
Comparison of Observed Number of Shots
Inside Zones Bounded by Circles of Radii
r i and ^ in., with Number Expected from
Bivariate Distribution with Radial Standard
Deviation a r , at four Ranges, R, in yd.
Test 1 (Ei and Es)
101
Test 1 (Mi and Ms)
102
A.6-7.
Comparison of Observed Number of Shots
Inside Zones Bounded by Circles of Radii
r^ and r ^ in., with Number Expected from
Bivariate Distribution with Radial Standard
Deviation <7 r , at four Ranges, R, in yd.
Test 2 (Ei and Es)
103
Test 2 (Mi and Ms)
104
A8.
Probabilities for Experts Firing Individually,
of Obtaining Exactly 1, 2, 3, 4, and 5 hits on
Type E Silhouette with Five -Shot Pattern
Salvo for Indicated Target Ranges
105
A9.
Probabilities for Marksmen Firing Indi-
vidually, of Obtaining Exactly 1, 2, 3, 4, and
5 Hits on Type E Silhouette with Five -Shot
Pattern Salvo for Indicated Target Ranges
105
ORO-T-160
47
TARGET RANGE DIAGRAM
Therange area can be described as a common- looking open-field area with gentle undulations
in the ground and with heavy grass, shrubs, and the like covering the surface area as one
would see in relatively open country in many parts of the world.
48
ORO-T-160
SiCURl
lTION
p
* fl**
BV1
d E s
i \J
SUMMARY
Results of expert riflemen and marksmen firing at man- size
targets at different ranges were analyzed to determine aiming
errors as function of range. The aiming errors in mils were
found to be independent of range. Results of the analysis were
used to compute the probability of hitting targets smaller than
the man-size target and, therefore, more realistically repre-
sentative of the average area presented by men in combat.
Results of the analysis were also used to predict the probabilities
of hitting targets with a hypothetical weapon firing a five -shot
pattern and a four -shot pattern salvo. The probability of obtain-
ing at least one hit from a single -salvo firing was found to be
decidedly greater than the probability of hitting with a single -shot
weapon. Probabilities of obtaining multiple hits with the salvo-
weapon were also computed. Finally, the effect of weapon disper-
sion on the probability of hitting was determined. These com-
putations show that eliminating the weapon- ammunition disper-
sion would not materially improve the rifleman's hit probability.
INTRODUCTION
In the BALANCE study of the Army weapons system, examination
of the basic hand arm of the infantry, the rifle, indicated a need to
study the effectiveness of aimed rifle fire on man-size targets at
ranges of combat interest. Heretofore, marksmanship has been
measured by scoring hits on target only, and sufficient evidence could
not be obtained on the nature of the dispersion (magnitude of errors)
of all rounds fired.
To provide basic parameters for the whole rifle study, a field test
was conducted at Fort Belvoir, Ya. , where expert riflemen and
marksmen were used in a series of experiments designed to provide
data from which meaningful conclusions could be drawn. Two grades
of riflemen (expert and marksman) were used so that by Army
standards the upper and lower limits of marksmanship could be
studied. By having the men fire on man- silhouette targets (type E)
at battle ranges of 100-300 yd on a transition type range, an element
of combat realism was provided. In order to record and measure
the dispersion of rounds, target screens 6 ft high and 12 ft wide
were mounted behind the silhouette target at each range. The
Appendix Frontispiece shows the design of the range used and the
manner in which targets were located.
ORO-T-160
49
" Mini 1 1 ^fON
Dimensions of the screens and test procedures were products
of preliminary trials designed to determine the methodology and
physical requirements necessary to study the man-rifle complex
on the desired basis. The target butts were draped with OD target
cloth so that rounds below the target and screen could be taken into
account by the perforations made in. the cloth. The target cloth also
was useful in camouflaging the mounds of earth at each target
location.
In the test plan, psychological factors which might have arisen
in group firing were eliminated by arranging groups of experts and
marksmen with equal representation on the fire line. Also, to
remove any learning effects in the experiment, the order of fire on
targets was arranged in a manner to follow a latin square type of
plan. This plan allowed each man to complete his firing serial on
four ranges by ending the serial on the target with which he had
begun, making a total of five target shoots on four ranges. Learn-
ing was not found to be a significant variable, and is not included
in the analysis.
Test personnel were selected according to marksmanship scores
from 13 training companies in the Engineer Replacement Training
Center, Fort Belvoir, Va. Sixteen riflemen (eight experts and eight
marksmen) were used on each of the two tests yriiich were conducted
on different days. Since different men were used in each test, a
total of 32 men were employed in the whole experiment. The follow-
ing outline shows the variety of conditions studied and the plan of
tests. The shots on target and screen were color-coded in each
experiment to make identification possible. All firing was done from
the prone position using M-l rifles and battle sights.
ANALYSIS
Objective
The objective of the analysis was to determine accuracy
of aimed rifle fire, and its dependence on target range, for
marksmen and experts firing the M-l rifle under the conditions
previously described. The accuracy thus obtained was required
as a basis for predicting with reasonable reliability, the
results which might be obtained with a hypothetical weapon of
comparable accuracy which could fire several bullets in a pre-
determined pattern.
Data from Tests
The locations of bullet holes, derived from the tests are
50
ORO-T-160
SECMfff 4HHf
PLAN OF RIFLE MARKSMANSHIP TESTS
Fort Belvoir, Va., 27 Oct and 10 Nov 1951
Plan of Testa 1 and 2
Purpose
Subject
Order of Fire
Conditions
To evaluate
E
A-B-C-D-A
Targets (silhouettes) exposed for 3 sec
individual
M
C-D-A-B-C
every 3 sec. For each exposure, each man
marksmanship
E
B-A-D-C-B
fired one round; 8 rounds fired per man per
M
D-C-B-A-D
target. Firing done in 4-man serials.
E
A-D-C-B-A
Conditions repeated.
M
B-C-D-A-B
E
D-A-B-C-D
M
C-B-A-D-C
E
A-B-C-D-A
Conditions repeated.
M
C-D-A-B-C
E
B-A-D-C-B
M
D-C-B-A-D
E
A-D-C-B-A
Conditions repeated.
M
B-C-D-A-B
E
D-A-B-C-D
M
C-B-A-D-C
To evaluate
8
B-A-D-C-B
Target exposed for 3 sec every 3 sec.
group
experts
Group fired simultaneously at each range,
marksmanship
single round firing for each exposure, 4
rounds per target per man.
8
B-A-D-C-B
Same conditions as for experts.
marksmen
Test No. 3
To study
4
C-A-C-C-A-A-C-A
Targets exposed for only 1 sec, alternate
effects of
marksmen
snap shooting at two target ranges,
rapid fire
schedule of exposure shown was unknown
when order of
to the men. Experiment was done for
target
group or simultaneous firing and for
appearance
is unknown
individual firing.
4
C-A-C-C-A-A-C-A
Same as above conditions.
experts
KEY
E Expert
M = Marksman
A ■= Tgt at 110 yd
3 = Tgt at 205 yd
C = Tgt at 265 yd
D = Tgt at 310 yd
ORO-T-160
51
INCHES
— ■if-™ tE(gFT^iiaHtittai»
[. | „ ^ f „
I >.
shown in Figs. A1 to A3Z, on which are also indicated the num-
ber of shots which were fired and the number of these which hit
the screen. In most of the tests, some of the rounds did not hit
the screen. Most, if not all, of these were observed to have hit
the ground in front of the screen. While the percentage of shots
hitting the target, as tabulated in the last column of Table A1 is,
of course, a function of accuracy, it does not provide complete
information on the nature of the dispersion of the shot -pattern.
Fig. Al— 110 yard range (Test No. 1), expert riflemen firing individually, 96 rounds fired
(8 each by 12 men), 96 rounds on target cloth, 88 rounds on target
> ft
i v
SECIIBIIiM(C(B£LttSS&» AT10N
52
ORO-T-160
-160 ORO-T-160
6
z
o
O-
ui
Fig. A2 — 205 yd range (Test No. 1), expert riflemen firing individually, 80 rounds fired (8 each by 10
men), 69 rounds on target cloth, 36 rounds on target
Unctenr»
Fig. A3— 265 yard range (Test No. 1), expert riflemen firing individually, 72 rounds fired (8
each by 9 men), 62 rounds on targer cloth, 34 rounds on target
Fig. A4 — 310 yard range (Test No. 1), expert riflemen
firing individually, 72 rounds fired (8 each by 9 men),
47 rounds on target cloth, 28 rounds on target
54
ORO-T-160
INI
J
*0 50
ids fired (8
Fig. A5 — 110 yard range (Test No. 1), expert riflemen firing simultaneously, 32 rounds fired
(4 each by 8 meri), 24 rounds on target cloth, 20 rounds on target
-T-160
«
ORO-T-I60
55
seMh SECIW THformatRW
securi
INFORMATION
|s 8(
’•j
Fig. A6— 205 yard range (Test No. 1), expert riflemen firing simultaneously, 32
rounds fired (4 each by 8 men), 26 rounds on target cloth, 12 rounds on target
1 rt f" 4 * s
inrijis
j t, vjt t y
Qlliu
56
ORO-T-160
iTION
51
MCMt
ION
usty, 32
target
Fig. A7 — 265 yard range (Test No. 1), expert riflemen firing
simultaneously, 32 rounds fired (4 each by 8 men), 21 rounds
on target cloth, 11 rounds on target
Fig. A8 — 310 yard range (Test No. 1), expert
riflemen firing simultaneously, 32 rounds
fired (4 each by 8 men)^ 19 rounds on target
cloth, 9 rounds on target
INCHES
40
pi ,, 110 yard range (Test No. 1), marksmen firing individuolly, 56 round. fir^ (8 ooch by 7 n.on) - 8 round.
Fig. A9— 1 in y«d '«9« l • round, on turgor dolk, 39 round, on turgor
u
I
o
30
20
10
10
20
INCHES
Fig. A9 110 yard rang© (Test No. 1), marksmen firing individually, 56 rounds fired (8 each by 7 men) -8 rounds
fired by Bates not included-56 rounds on target cloth, 39 rounds on target
O
V
O
H
O'
o
Fig* A10— 205 yard range (Test No. 1), marksmen firing individually, 72 rounds fired (8 each by 9 men), 58 rounds
on target cloth, T9 rounds on target
<ji
\D
SECURITY
SECURITY
INFORMATION
piper
luOoj
iO
* K
iTiprf
! I a %uil
Fig. All 265 yard range (Test No. 1), marksmen firing individually, 72 rounds
fired (8 each by 9 men), 65 rounds hit target cloth, 25 rounds hit target
Fig. A12 310 yard range (Test No. 1), marksmen firing
individually, 80 rounds fired (8 each by 10 men) -Bates
excluded, 61 rounds on target cloth, 24 rounds on target
i tvi ft
uIaSo!ll0(
60
ORO-T-160
RATION
ORO-T-160
I
H
t
I—*
o
©
flu
J L
J L
Fig. A13 — 110 yard range (Test No. 1), marksmen firing simultaneously, 32 rounds fired (4 each by 8 men), 30 rounds hit target cloth,
12 rounds hit target
WMATION
ORO-T-160
r
Fig* A14 — 205 yard range (Test No. 1), marksmen firing simultaneously, 32 rounds fired (4 each by 8 meni
19 rounds on target cloth, 4 rounds on target
mm
w
i /r* f
! . Nl
Fig. A15— 265 yard range (Test No. 1), marksmen firing simultaneously, 32 rounds fired (4 each by
8 men), 32 rounds hit target cloth, 6 rounds hit target
Fig. A16 — 310 yard range (Test No. 1), marksmen firing simultaneously,
32 rounds fired (4 each by 8 men), 25 rounds hit target cloth, 4 rounds
hit target
ORO-T-160
63
Fig* AI7 — 110 yard range (Test No* 2), expert rifletnen firing individually, 96 shots fired
(8 each by 12 men), 91 rounds hit target cloth, 81 rounds hit target
64
pH 1
ORO-T-160
IATION
Fig. A18 — 205 yard range (Test No. 2), experts firing individually, 64 rounds fired
(8 each by 8 men), 45 rounds hit target cloth, 22 rounds hit target
ORO-T-160
65
SECI
INCHES INCHES
INFO'Ri
Fig. A19 — 265 yard range (Test No. 2), expert riflemen firing
individually, 64 rounds fired (8 each by 8 men), 56 rounds on
target doth, 30 rounds on target
Fig. A20 — 310 yard range (Test No. 2), expert riflemen firing
individually, 80 rounds fired (8 eoch by 10 men), 77 rounds hit
target doth, 35 rounds hit target
66
ORO-T-160
ION
iMATION
*
Fig. A21 — 110 yard range(Test No. 2), experts firing simultaneously, 32 rounds fired (4 each
by 8 men), 28 rounds hit target cloth, 28 rounds hit target
n r* I o o c* ifi £j i
I ii/lQwOli IbU
ORO-T-160
67
ORO-T-160
CD
\
Fig. A22 — 205 yard range (Test No. 2), experts firing simultaneously, 64 rounds fired (4 each by 16 men),
58 rounds hit target cloth, 19 rounds hit target
Fig. A23 — 265 yard range (Test No. 2), expert riflemen firing
simultaneously, 32 rounds fired (4 each by 8 men), 28 rounds
on target cloth, 13 rounds on target
Fig. A24 — 310 yard range (Test No. 2), expert riflemen firing
simultaneously, 32 rounds fired (4 each by 8 men), 25 rounds
hit target cloth, 8 rounds hit target
ORO-T-160
69
INCHES
m
TION
Fig. A25 — 110 yard range (Test No. 2), marksmen firing individually, 64 shots fired (8 each
by 8 men), 64 rounds hit target cloth, 34 rounds hit target
70
GRO-T-160
ATION
09 t-l-o*o
1
1
1
1
Fig* A26 — 205 yard range (Test No. 2 ), marksmen firing at target individual ly, 72 rounds fired (8
each by 9men) / 59 rounds hit target cloth, 12 rounds hit target
INFORMATION
10
0
30
20
10
0
10
20
30
40
50
60
70
INCHES
Fig, A27 — 265 yard range (Test No. 2), marksmen firing individually, 96 rounds fired
(8 each by 12 men), 88 rounds on target cloth, 19 rounds on target
30 20 10 0 10 20 30 40 50 60 70
INCHES
Fig, A28 — 310 yard range (Test No. 2), marksmen firing
individually, 80 rounds fired (8 each by 10 men), 61 rounds
hit target cloth, 12 rounds hit target
70
60
50
K 40
20
10
0
72
SEC
poi*
by 16 men) - 1 man fired 5 rounds -49 rounds hit targetcloth, lOrounds hit
Fig. A31 — 265 yard range (Test No. 2), marksmen firing
s imultaneous I y f 32 rounds fired (4 each by 8 men), 24
rounds hit target cloth, 8 rounds hit target
Fig. A32 — 310 yard range (Test No. 2), marksmen firing
simultaneously, 32 rounds fired (4 each by 8 men), 26 rounds
hit target cloth, 2 rounds hit target
ORO-T-160
75
x (IN.)
and Dispersion (Standard Deviation)
As already indicated, the location of those rounds which did
not hit the target or screen, is, of course, unknown. How then
can the mean (mpi) and dispersion (standard deviation) be deter-
mined when these depend on the actual location of all shots? This
problem is most conveniently solved by using probability paper as
illustrated in Fig. A33.
STANDARD DEVIATION (OR MEANS) LESS THAN THAT INDICATED BY ORDINATE, %
Fig. A33 — Example illustrating use of probability paper to determine standard deviations
and means, whether or not distribution is truncated. Data are from Test 1, experts firing
individually at 205 yd.
Suppose x is a variable normally distributed about mean x,
and suppose from a sample of n x's F, is determined, where F t
is the fraction of all the x's in the sample which have values less
than x t , and F, the fraction containing all values of x less than
Xj (x t >> x t )and so on to F n . Then for a normal distribution of the
x's, the scale of F (abscissa scale of Fig. A33) is so designed
that when values of F are plotted against the corresponding x ,
the points determine a straight line. The ordinate, on this line,
corresponding to abscissa F =50 (i. e. , 50 percent) determines
60
.01 o.i
5 10 20 30 40 50 60 70 80 90 95 98 99 99.9 99.99
76
ORO-T-160
y (IN.)
r
the mean of the sample. If this mean is subtracted from the
ordinate corresponding to abscissa F = 0.841, the difference is
the estimated standard deviation of individual values about the
mean of the sample.
Thus, the upper line in Fig. A33 indicates mean: x = -0.5 inch
and standard deviation: S x = 13.5 in. These apply to the x coordinates
of the points of Fig. A2. Similarly from the lower line in Fig. A33:
y = 16.0 inches (y measured from bottom of screen in Fig. A2) and
S y = 15.0 inches. The percentages (i. e. , abscissae) for the points
along the lower line of Fig. A33 were computed using as base (i. e. ,
100 percent) the total number of shots fired (i. e. , 80 from Fig. A2),
although of these (11/80) 14 percent were off the screen at the
bottom. Thus, even though the distribution of y ' s is truncated at
y - o (bottom of screen), it is relatively simple to estimate the
mean and the standard deviation through the use of probability paper
which incidently facilities the calculation even for the nontrun-
cated case.
On the other hand, if the distributions of x and y are statistically
independent (as was the case of Fig. A1 for which the correlation
between x and y did not significantly differ from zero) then, refer-
ring to Fig. A2, the mean and standard deviation of x will be
independent of y. Hence, in computing the percentages (ordinates)
for the upper set of points in Fig. A33, it was essential to use a
base (i. e. , 100 percent) equal to the number of shots on the screen
(i. e. , 69 from Fig. A2). That is to say, the distribution of the
x’s of Fig. A2 is not truncated, as was that of the y’s; only the
sample size for x is diminished as a consequence of some 11
shots having gone off the screen.
Summary of Means and Standard Deviation
Proceeding as described in the preceding paragraph, the means
of x and y and their standard deviations were determined for each of
the test results shown in Figs. A1 to A32. For Tests 1 and 2, the
results are given respectively in Tables A1 and A2. Inspection
of S x and Sy(i. e. , the standard deviations of x and y) in Tables
A1 and A2 indicates on the whole no very great difference between
S x and Sy . More elaborate tests indicate the same conclusion.
For example, in Test 1, Table 1, if S x and Sy in the first four
rows are each normalized to range 100 yd (on the assumption of
constant mil error), and then the variance of x and y are sepa-
rately pooled (from the results at the four ranges), the resulting
S x = 4.9 inches and S y = 5.8 inches, a difference of only 18 per-
cent. In other cases, for example, in Test 1 for marksmen
ORO-T-160
77
iILPJ
t Jf O Q ( T f p W
firing individually, (M,, Table Al) S exceeds S . Hence, on the
whole no serious consequences are likely to arise from assuming
°x = a y * or the results (a x , and <r y are standard deviations for
the whole population).
Dispersion as a Function of Range
In the preceding paragraph, it was indicated that when the
standard deviation in x (or y) at each of the four ranges was
divided by the range, the results were essentially independent
of range. It was also indicated that x and y were independent
Fig. A34— -Observed standard deviation, S r , of distance of individual
shots from mpi as function of target range, for experts. °, Test 1; +,
Test 2; I, centered at from combined results of Tests 1 and 2.
Total vertical extent of 1 indicates range within which 50 percent of
results from similar samples should fall.
1 * 1
\ p n
fr <4 Li ..
L [ P.
78
ORO-T-160
(i. e. . correlation zero) and that their standard deviations could
be assumed equal. This suggests the standard deviation of
r (r* = x 2 + y J ) as a convenient measure of dispersion since it
combines S x and S y (actually S r * = S y J + S x a ).
For Tests 1 and 2 respectively, values of S r are listed in
column 7 of Tables A1 and A2. In Figs. A34 and A35, these
values of S r are plotted as a function of range to target. It is
evident in Figs. A34 and A35 that the "observed" values of
for the different ranges are, within the indicated statistical
uncertainties, reasonably approximated by the indicated straight
lines. This implies that the dispersion (standard deviation) in
inches at the target increases linearly with the target range,
according to the equations indicated. The constants show that,
in accuracy, the riflemen rank in the following order: (1) experts
firing individually, (2) experts firing simultaneously, (3) marks-
men firing individually, and (4) marksmen firing simultaneously.
Systematic Errors in the mpi
Figure A36 indicates the vertical distance of the mpi from
the top of the target, at the four ranges, for experts and marks-
men in Tests 1 and 2. Even if all men aimed at the center of
the target, vertical systematic deviations of the mpi from the
aiming point would be expected as a consequence of the parabolic
nature of the bullet trajectory. How the vertical coordinate of
the mpi varies with range would depend on the range for which
the sights are set. Figures A37 and A38 indicate for Tests 1
and 2, respectively, the x - coordinate of the mpi at different
ranges. It is evident that in Test 1 the bias is quite small' and
in most cases probably not statistically significant. On the
contrary, the bias in Test 2 is generally larger than in Test 1,
particularly for marksmen, and is in many cases statistically
significant. Results of tests for the significance of this bias are
given in the last row of Tables A4, A5, A6, and A7, on which
further comment will follow.
Comparison of Observed and
Theoretical Distributions of Deviations from mpi
If x and y are deviations from a mean, and are independently
and normally distributed with equal standard deviations, a x = a ,
then it is convenient to consider the distribution of radial y
deviations, r, ^(r = x + y ), which have standard deviation,
°r = (°x* + CT y*)^- 14 can be shown that, of all the radial deviations
ORO-T-160
79
INCHES INCHES
flwwSECItlT
0 100 200 300 400
RANGE (YD)
Fig. A35 — Observed standard deviation, $ r , of distance of individual
shots from mpi as function of target range for marksmen. For meaning
of symbols see Fig. A34.
80
ORCUT-160
from the mean, the fraction having deviations greater than or
equal to kv r is, on the average, given by:
W(k) = e (1)
or looked at in another way W(k) is the probability that a shot
falls outside the circle of radius r = kt7 r . The following table
indicates values of W(k) for a few selected values of k:
k
0.000
0.536
0.833
1.179
DO
W (k)
1.000
0.750
0.500
0.750
0.000
In particular, the circle of radius 0.833 a r , with W(k) = 0.500,
is usually called the circular probable error (cpe). Thus circles
of radii, o, 0.536 a r , 0.833 a T , 1.179 a r , and «, with centers at
the mpi, divide the plane into four zones, such that the proba-
bility of a shot hitting within any one of the zones is 25 percent.
These circles were drawn in each of the originals of Figs. A1
to A32, (but they are not reproduced here), and the radii of the
circles bounding each zone are listed in Tables A4, A5, A6,
and A7. These tables also indicate the expected and observed
numbers of shots falling in each zone.
In several cases, such as illustrated in Fig. A4, parts of some
or of all zones are off the screen. For these cases it is obviously
impossible to indicate how those shots which did not hit the screen
were distributed among the zones. In such instances only those
shots observed to hit the screen can be properly allocated among
the partial zones which are on the screen. The expected number
of hits within the parts of zones which are on the screen is, how-
ever, computed from the total number of shots fired (72 in the
case of Fig. A4). This was done using circular probability paper
to facilitate the numerical integration to determine the probability
of hits falling within the partial zones. Multiplying these proba-
bilities by the total number of shots fired gave the expected num-
ber of hits in each partial zone.
Corresponding to each of Figs. A1 to A32, the discrepancy
between the observed and expected number of hits in each of the
four zones (or partial zones) was measured by y 1 . P (*.*) in
Tables A4, A5, A6, and A7 indicates the probability of obtaining,
in similar samples, as bad or a worse fit between observation
and expectation than that indicated in the Tables. For Test 1,
the values of P (y a ) in Tables A4 and A5 are, in general, large
enough so that the fit of the observed distribution to the theoret-
ical one is acceptable. Thus, for subsequent calculations, the
ORO-T-160 81
1AT10N
more convenient theoretical distribution can with confidence be
used in place of the observed distribution. The discrepancy
between the observed and theoretical distributions in Test 2 are
on the whole greater than for Test 1.
Undoubtedly, this arises either from a large bias in the mpi
for shots fired by some of the riflemen, or from nonhomogeneity
in the dispersion for all the riflemen. However, as Figs. A34
and A35 indicate, the radial dispersions, s r , are not very differ-
ent in the two tests so that subsequent conclusions based on dis-
persion indicated by the straight lines (or equations) of Figs. A34
and A35, will not be much in error.
Remarks on the Homogeneity
of Results for Individual Riflemen
Attempts were made to identify each bullet hole according to
the man firing in the case of those tests in which men fired indi-
vidually. In many cases, it turned out that holes were obviously
improperly marked. Because of the small number of shots fired
by each man, the results of individuals could be compared reli-
ably only if the location of all shots fired was known. Thus, the
comparison of individuals is limited to the situation of Figs. A1
and A9. The test for homogeneity consisted, in the case of Fig.
Al, in counting the number of shots each individual fired inside
and the number outside the probable error circle, and testing
this against the expected number based on the results for all
riflemen. The following table indicates the results for Fig. Al:
Man No.
1
2
3
4
5
6
7
8
9
10
11
12
Total
No. inside 9,
p.e. circle
0
4
4
5
2
5
7
7
5
6
1
2
48
No. outside a
p.e. circle
8
4
4
3
6
3
1
1
3
2
7
6
48
a The expected number throughout is 4.
Applying the y s test, P = 0.003, for the hypothesis that there
is no difference (in the long run) among the several individuals,
the value of P indicates a likelihood of some difference among
the individuals, which for subsequent purposes is not serious,
mainly because some individuals (Nos. 1 and 11) appear worse
than the average, while others (Nos. 7 and 8) appear better.
This somewhat compensates, so that the distribution of all
shots does not deviate seriously from the expected distribution
82
ORO-T-160
N
(see P (y 1 ) Tables A4, A5, A6, and A7). Similar tests for the
results in Fig. A 9 are given in the following table:
Man No.
1
2
3
4
5
6
7
Total
No. inside a
p.e. circle
1
4
5
4
7
2
4
27
No. outside a
p.e. circle
7
4
3
4
1
6
4
29
a The expected number throughout is 4.
Here P (y 2 ) = 0.08, indicating no statistically significant depar-
ture from homogeneity of results for the seven individuals.
Remarks on Deviations of mpi from Aiming Point
In connection with Fig. A36, it is reasonable to expect some
systematic vertical deviations in mpi with range; because of
this, tests of the vertical deviation of the mpi from an aiming
point were not made. However, deviations of the mpi to the
right or left (x coordinate) from the vertical line through the
center of the target were tested to determine whether they were
large enough to be statistically significant. The results are
shown in Tables A4, A5, A6, and A7 in which P (x) indicates
the probability of obtaining (in further samples under similar
circumstances) deviations of the mpi as great or greater than
those actually observed. It is evident in Tables A4 and A5 that,
in most cases, the deviations are not statistically significant.
For Test 2 as shown in Tables A6 and A7 several small values
of P were obtained. This indicates that many of the deviations
are statistically significant, particularly since Table A2 and
Fig. A37 show that all the mpi, in Test 2, deviated to the
right (x, positive). It should be mentioned, however, that if
the mpi for some of the individual riflemen deviate significantly
from the mpi averaged for all, then the deviations of single
shots from the latter mpi are not statistically independent.
Taking account of this would increase the values of P (x) in the
Tables. In any case, the deviations of the mpi (x in Tables A4
and A5) in Test 1 were not, in general, significant so that
subsequent calculations will apply reasonably well to conditions
of Test 1.
ORO-T-160 83
10
-X-
100
J-
300
400
200
RANGE (YD)
(§) Experts 0 Marksmen
Fig* A3 6 — Distance of mpi from top of target as function of range;
combined individual and simultaneous firings of experts and marksmen;
Tests 1 and 2.
84
9C<
ORO-T-160
INCHES , INCHES
mm
15
10
5
0
-5
10
0 100 200 300 400
RANGE (YD)
O Experts firing individually A Marksmen firing individually
X Experts firing simultaneously O Marksmen firing simultaneously
15
10
5
0
”5
-10
0 100 200 300 400
RANGE (YD)
Fig* A37 — Distance of mpi from vertical line through target center as
function of range; marksmen and experts firing individually and
simultaneous ly, Test 1*
ORO-T-160
85
INCHES INCHES
*^%*ECimnr
O Experts firing individually
X Experts firing simultaneously
A Marksmen firing individually
□ Marksmen firing simultaneously
Fig. A38 — Distance of mpi from vertical line through target center as
function of range; marksmen and experts firing individually and
simultaneously. Test 2.
86 » C ORO-T-160
L’ !■ ’
^'■ yuamnn S ra t H - " mPMMtioN
siLuimii 5TIIIEI 11,1 lUiuiuMMi
Comparison of Observed and Theoretical
Probabilities of Hitting Target at Various Ranges
Figures A39 and A40 compare the observed and theoretical
probabilities of hitting the target at different ranges under the
several conditions involved in Tests 1 and 2. The observed
probabilities are, of course, just the percentage hits on the
target, from Fig. A1 to A32. The theoretical probabilities,
shown by the curves of Figs. A3 9 and A40 were computed on
the basis of the following model: (a) The target was assumed
to have the shape and dimensions shown in the accompanying
sketch:
The location of the assumed mpi for all ranges is shown;
it is on the vertical center line through the target, (b) The
standard deviation of radial deviations, for any particular
range, was assumed to be that given by the lines (or equations)
in Figs. A34 and A35.
Tests show that the deviations of some of the "observed
points" from the curves, in Figs. A39 and A40, are statisti-
cally significant. These deviations are generally below the
curve. In Fig. A40, for example, all the crosses in the upper
figure fall below the curve. Examination of Table A2 indicates
that the mpi (the x's in the Table) were all to the right of the
vertical center line through the target; moreover, the small
values of P (x) in Table A7 indicate that these deviations of the
ORO-T-160
87
*™» S M HEf
tATSON
PROBABILITY
Fig. A39 — Probability of expert riflemen hitting Type E silhouette of range. Ei: firing
individually; Es: firing simultaneously.
88
ORO-T-160
isq
S K RET WMfeRTION
PROBABILITY
Fig. A40 — Probability of marksmen hitting Type E silhouette target as a function of
range. Mi: firing individually; Ms: firing simultaneously.
ORO-T-160
89
mpi from the center line were statistically significant. Never-
theless, the curves give a fair approximation to observed
results, at least for Test 1. In fact, the differences between
the theoretical probabilities of hit and those observed in Test 1
are, in general, comparable with the differences between the
observed probabilities in Test 1 and those observed in Test 2.
At the range of 205 yd, all the observed points fall below the
curves. In Figs. A34 and A35 it may also be seen that the
observed standard deviations obtained for range 205 yd, appear
to be consistently high. Observers at the firing range indicated
that the target appeared to be as far away as that at 265 yd.
This may have been an illusion due to some bushes close to
the line of sight. If sufficient data were available to determine
from a large number of samples the nature of the distribution of
mpi, this could be used in the determination of theoretical proba-
bilities. In any case, the theoretical curves and the hypotheses
on which they were derived provide a convenient and sufficiently
good basis on which to compare probabilities of hitting targets
with a single-shot weapon and a hypothetical one which fires
several shots simultaneously in a pattern.
Remarks on Results of Firing on Targets
Appearing Randomly at Either of Two Ranges
Table A3 indicates the results obtained when the target (type
E silhouettes) appeared randomly, and for 1 sec. , at either of
two ranges (110 yd or 265 yd) as described in the introduction.
Due to the small number of rounds fired and especially to the
very small number of hits on the target, inspection of Table A3
indicates that for any particular range the differences between
the percentage hits on the target are not statistically significant
for experts firing individually (Ej) compared to experts firing
simultaneously. For Test 3 the same conclusion obtains for
marksmen. Thus, from Table A3 the results Ej and E a were
combined for each of the two ranges; results for and M s
were similarly combined. When the combined results for
experts in Test3 at range 110 yd were compared with the results
of experts firing simultaneously from Tests 1 and 2, at 110 yd,
the percentage hits on the target were definitely less in Test 3,
and the difference was found to be statistically significant. Simi-
larly, the combined results for experts in Test 3 at 265 yd
indicated a significantly lower percentage hits than that obtained
from the combined results, in Tests 1 and 2, of experts firing
90
ORO-T-160
simultaneously at range 265 yd. That is, as would be antici-
pated, the accuracy of expert riflemen for the same range was
much less under the conditions of Test 3 than under the conditions
of Tests 1 and 2. For the marksmen, the results from Test 3
were not statistically different from those of Tests 1 and 2
at the same ranges.
APPLICATION
Theoretical Probability of Hitting
Type E Silhouette Target With a Salvo Pattern
In the same way that the results of the present analysis were
used to compute the curves of Figs. A39 and A40, they may also
be used to obtain the variation, with range, of the probability
of hitting the target with a salvo pattern. In Fig. A41, the curves
M„(l) and E t ( 1 ) are respectively the curves M s of Fig. A40, and
Ej of Fig. A39. The curves M s (l) and Ej(l) were obtained for the
target, sketched previously, in the following way: The right half
of the target can be considered made up of two rectangles: one 5
in. x 38 in. , and the other 5 in. x 28 in. ; with A as mean, the
independent probabilities of x and y falling inside each of the rec-
tangles are readily found from tables of the probability integral
since the standard deviations of x and y are known for any range;
for each rectangle the product of the two probabilities gives, of
course, the probability of both x and y being in the rectangle;
summing over both rectangles and multiplying by 2 gives the
probability of hitting the target.
In Fig. A41, the curves Ej(2) and Mg (2) were computed for
the five -shot pattern drawn as it would hit a screen at 300 yd
range. It was assumed that there was no statistical dispersion
in the position (at the target) of any one of the individual missiles
relative to the others. It was also assumed that the "spread" of
the pattern was proportional to range. The dispersion of the
center missile (the others in the pattern remain fixed relative
to the center missile) at the target was assumed to be the same
as that used in computing the curves E { (1) and M s (l), i. e. , that
derived from the analysis of the aiming errors obtained in the
tests. For each range a "virtual target" was drawn such that
if the aimed round of the pattern (i. e. , the central one) fell
inside the boundary of the virtual target then at least one missile
hit the target. Except for the fact that the "virtual target" was
somewhat more complex in shape, the procedure used to obtain
ORO-T-160
91
PROBABILITY
SECURITY
INFORMATION*
92
Fig. A41 — Probability of hitting E type silhouette target with single
shot compared with probability of at least one hit with a five-shot
pattern salvo; curves based on aiming errors. E*: experts firing indi-
vidually; M s : marksmen firing simultaneously; (1) with single shot;
(2) at least one hit with five-shot pattern I; (3) at least one hit with
five-shot pattern II.
ORO-T-160
secu ;
iRMATJpN
PROBABILITY
SECURl
Unclassified
the probability of obtaining at least one hit was the same as that
described above for single shots (i. e. , no pattern).
The curves Ej (3) and M g (3) were similarly computed for
the same shape of salvo pattern, but for a pattern with half the
spread (at any given distance) as that used for E t (2) and M a (2).
From Fig. A41 it is evident that, of the two shot patterns, the
one with the greater spread has the over -all advantage over
ranges up to 300 yd. Incidentally, the probability of at least
one hit, on type E silhouette, indicated by curves E. (2) and
M s (2), Fig. A41, for ranges up to 225 yd applies also to the
four -shot pattern resulting from removal of the center shot from
pattern I. Curves Ej (3) and M a (3) apply also to the four -shot
pattern resulting from the removal of the central bullet of
pattern II.
Probabilities for 1. 2. 3, 4, and 5 Hits
on Man-Size Target With Five -Shot Pattern Salvo
The probabilities of 1, 2, 3, 4, and 5 bullets hitting a
target are given in Tables A8 and A9 for marksmen and for
experts individually firing a five -shot pattern salvo. The
target, type E silhouette, is that sketched previously. The
shot pattern used in the calculations is pattern I as sketched
in Fig. A41. It should be noted that, in the case of multiple
hits, the individual hits are not located at random relative to
each other. This follows from the assumptions stated previously
to the effect that on arrival at the target the relative positions of
all missiles in the pattern are fixed, with the dimensions of the
pattern proportional to range.
Comparison of Theoretical Probabilities of Hitting
"Average Target" with Single -Shot and Five-Shot Pattern Salvo
At the eye of a rifleman, the solid angle subtended by the
average human target in combat is less than that subtended by
the type E silhouette. 1 For the approximation to the average
target a rectangle (for convenience in calculation) 20 in. x 12 in.
was chosen and designated target A (see Fig. A42). The proba-
bility of hitting target A as a function of range was computed giving
the results shown by the curves in Fig. A42. These curves indicate
that the probability of at least one hit with the five -shot pattern
salvo is decidedly greater, for the same range, than the probability
of hitting with a single shot. If the central bullet is removed from
l ORO-R-5
ORO-T-160
93
PROBABILITY
SECURI^tKHW^FORMATION
1
RANGE (YD)
CO
<
CO
O
£L
Fig* A42 — Probability of hitting “average" target, A, (sketched in
box) with single shot compared with probability of at least one hit on
target with five-shot pattern salvos. E j : experts firing individually;
M $ : marksmen firing simultaneously; (4) with single shot; (5) at least
one hit on target with five- shot pattern I.
94
ORO-T-160
SECI
In
the five -shot pattern the probability of at least one hit on target A
is unaffected at ranges less than 150 yd.
Remarks on Significance of Probabilities of Hitting a Target
with a Single-Shot and with Five-Shot, Four -Shot Pattern Salvos
Although the probability of at least one hit on the target is, at
the same range, greater for one five -shot pattern salvo than for
a single shot, it is less then the probability of at least one hit on
the target for five separately aimed single shots. Consider, for
example, the comparison at 200 yd range for the upper curves in
Fig. A42. For the five -shot pattern, curve Ej(5) indicates at
200 yd a probability of about 0.74 for at least one hit. For one
single shot, curve Eg (4) indicates about 0.32 for the hit probability.
The probability of at least one hit in five single-shot trials is then:
(1 - 0.68*) = 0.85 which is somewhat greater than the probability
of 0.74 for at least one hit for the five-shot pattern.
Consider also the case for range 150 yd for target A. The curve
Eg (4) of Fig. A42 shows for range 150 yd a probability of 0.49 for
hitting target A. Curve E. (5) indicates 0.90 for the probability of
at least one hit using the five-shot pattern. As indicated in the
preceding section, the probability of at least one hit for the four-
shot pattern (central one of the five-shot pattern removed) is, for
ranges less than 150 yd, the same as for the five-shot pattern.
Thus, the probability of at least one hit, in this case, from five
single shots is (1 - 0.51 s ) = 0.97 which is slightly greater than that
for at least one hit from a single five -shot pattern salvo. However,
if we use a four-shot pattern we find (1 - 0.5 1 4 ) = 0.93 for the proba-
bility of at least one hit from four single shots compared to 0.90
for the probability of at least one hit from the four -shot pattern.
Thus, for targets which may remain in the rifleman's view only
long enough for him to aim once, the advantages of the five -shot
pattern salvo are evident.
Effect of Weapon Dispersion on Probability of Hitting Target
In order to determine the effect of weapon dispersion (the
dispersion at the target when the rifle is rigidly fixed) on the
probability of hitting the target, it is necessary to determine the
standard deviation due only to aiming. From the firing test data
the total standard deviation, a t , at the target was found to be
proportional to the range, that is
a T ~ cr in. (l)
with r the range in units of 100 yd.
• » i * Jjf
ORO-T-160 95
SEC I
»<B«
Let tr w represent the standard deviation due to weapon dispersion
(i. e. , standard deviation of shot distances from mpi). Now the
standard deviation at the target, due only to weapon dispersion,
will also be proportional to the range r, then:
Also the standard deviation, <7 A , due to aiming errors only (i.e.,no
weapon -ammunition dispersion) will be proportional to the range, thus:
Since deviations from the mpi due to aiming errors and to weapon-
ammunition errors are independent, than at a particular range:
Tests on the M-l rifle indicate that a= 2.3 in.; that is, the
standard deviation of shot distances from the mpi, for a rigidly
held rifle, is 2.3 in. at 100 yd. (i.e., r = 1), including dispersion
due to ammunition. This determines A in Equation 5 when c is
known. From Table A5 the value of c is 9.0 in. for marksmen
firing individually. For this case, and using oc= 2.3 in., Equation
5 determines A = 76. Thus for other weapon dispersions, k x 2.3,
the variance^ 2 of the combined errors due to weapon- ammunition
and aiming is given by:
Consider target A which, as previously described, is a rectangle
20 in. x 12 in. The probability of hitting this target (mpi at center)
is, to a degree of approximation sufficient for present purposes, the
probability of hitting a circular target with the same area. Thus,
for convenience in estimating the effect of weapon dispersion on
probability of hitting, consider the circular target with radius a
such that it s? = 240 in. 2 , (12 in. x 20 in.) from which a 2 = 76.5
(a = 8.75 in.). For the mpi at the center of the circle, the probability,
P m , of missing the target (i.e. , of shots falling outside the circle
of radius a) is:
for marksmen firing individually. The three lines designated
cr w = Otr in.
( 2 )
= At in.
(3)
o;
T
2
a K + <
2
(4)
or for any range r:
A 2 r* +0tk 2 r 2
(5)
'r
2
= r 2 (76 + 5k 2 )
( 6 )
p.
m
e
-76.5/r*(76 + 5k 2 ) ^
in Fig. A43 are the curves of Equation (7) for each of three values
96
ORO-T-160
5EO
M&MfwaiftyioN
3 :
y*
o
QC
<
O
z
I-
LL
O
_J
cfi
<
£0
O
Q£
CL
Fig. A43 — Probability of hitting a circular target of area = 240 sq in. (radius = 8.75 in.)
as a function of range for several weapon-ammunition errors. Plotted for marksmen
firing individually, Mj; and experts firing individually, Ej. k is a selected multiple of
the standard deviation of the strike from the mpi, as caused by weapon and ammunition
alone. Thus k - 1 represents actual performance with issue rifle and ammunition, k =0
shows performance with perfect weapons and ammunition, and k = 2 indicates
performance with weapons and ammunitions giving double the actual standard deviation.
of k. From these curves (Mj) it will be seen that the probability
of hitting for K = 0 (i.e., no weapon -ammunition dispersion) is
only slightly less than k = 1 (i.e., for the actual dispersion of
the M-l rifle and ammunition). Also, the curves for k = 2
indicate probabilities of hitting which are still not significantly
less than those for a dispersionless rifle and ammunition (k = 0).
The four lower curves (Ej) in Fig. A43 apply to experts firing
individually, for which the equation is:
P = e " aV V = e -76.5/r»(42.5+5k 2 )
m ' *
Equation 8 is obtained in the same manner as Equation 7 starting
with the value of 6.9 in. for c, obtained from Table A4 for experts
firing individually.
ORO-T-160
ORO-T-160
00
TABLE A1
RIFLE RANGE TEST 1
Men
Range,
y*
Std.
Deviation, in.
No. Men
Rounds
Total
No* Rounds
% on
yd
/ in*
in.
X
y
r
Firing
per man
Rounds
Target
Screen
Target
E i a
110
- 0.9
13*5
4.1
5.2
6.4
12
8
96
88
96
0.917
205
- 0.5
16.0
13.5
15.0
20.2
10
8
80
36
69
0.450
265
~ 3.0
19.5
13*0
13*0
18.4
9
8
72
34
62
0.472
310
+ 6.0
7.0
12.6
17.8
21.8
9
8
72
28
47
0.389
E s b
110
+ 1.2
8.7
4.1
11.2
11.9
8
4
32
20
24
0.625
205
- 2.8
15.6
11.0
12.8
16*9
8
4
32
12
26
0.375
265
- 5.9
11.0
8*4
17.2
19.1
8
4
32
11
21
0.344
310
- 8.2
10.0
15*0
18.3
23.7
8
4
32
9
19
0,281
Mi e
110
- 1.7
16.4
8.7
6.4
10.8
7
8
56
39
56
0*696
205
- 2*0
15.2
13*0
14.5
19.5
9
8
72
19
58
0.264
265
+ 4.8
18.3
17*2
14.0
22*2
9
8
72
25
65
0.347
310
- 1.0
14.8
24.0
12.2
26.9
10
8
80
24
61
0*300
M s d
110
- 1.8
14.2
14.2
9.0
16.8
8
4
32
12
30
0.375
205
+ 10.5
11.8
23.0
20.2
30.6
8
4
32
4
19
0*125
265
- 2.5
31.5
25.1
13,9
28.7
3
4
32
6
32
0.188
310
+ 1.0
17.2
36.0
15.8
39.3
8
4
32
4
25
0.125
- Expert Riflemen Individually Firing at Target. - Marksmen Individually Firing at Target.
E g - Expert Riflemen Simultaneously Firing at Target. - Marksmen Simultaneously Firing at Target.
ORO-T-160
TABLE A2
RIFLE RANGE TEST 2
Men
Range,
yd
x,
in.
y *
in.
Std.
Deviation, in.
No. Men
Firing
Rounds
per man
Total
Rounds
No. Rounds
% on
Target
X
y
r
Target
Screen
E. a
110
+
0.6
15.4
5.2
6.9
8.6
12
8
96
81
91
0.844
1
205
+
5.7
18.0
14.8
14.5
20.7
8
8
64
22
45
0.344
265
+
3.4
14.1
9.4
13.1
16.1
8
8
64
30
56
0.469
310
+
12.5
23.5
13.5
13.1
18.8
10
8
80
35
77
0.438
E s b
110
+
0.8
20.5
2.8
9.3
9.7
8
4
32
28
28
0.875
205
+
3.9
23.0
17.1
14.3
22.3
16
4
64
19
58
0.297
265
+
1.7
17.0
10.1
12.8
16.3
8
4
32
13
28
0.406
310
+
2.5
13.9
21.5
14.1
25.7
8
4
32
8
25
0.250
Mj c
110
+
5.8
23.4
6.8
7.1
9.8
8
8
64
34
64
0.531
205
+
14.1
26.6
23.1
17.9
29.2
9
8
72
12
59
0.167
265
+
15.2
20.2
19.5
11.4
22.6
12
8
96
19
88
0.198
310
+
19.1
17.0
24.1
23.3
33.5
10
S
80
12
61
0.150
M d
no
+.
2.2
26.7
10.5
8.1
13.3
8
4
32
18
29
0.562
s
205
+
12.1
24.5
18.5
18.0
25.8
16
4
65 e
10
49
0.154
265
+
9.2
14.4
12.7
20.1
23.8
8
4
32
8
24
0.250
310
+
10.8
21.3
17.2
23.7
29.3
8
4
32
2
26
0.062
®E. - Expert Riflemen Individually Firing at Target, - Marksmen Simultaneously Firing at Target.
b E 1 g - Expert Riflemen Simultaneously Firing at Target. e Qne Man Fired Five Rounc *s.
C M. - Marksmen Individually Firing at Target.
100 ORO-T-160
TABLE AS
RIFLE RANGE TEST 3
FIRING AT TARGETS NO* 1 AND NO. 3 ALTERNATELY ON RANDOM SCHEDULE
Men
Range,
yd
x,
in.
y *
in.
Std.
Deviation, in.
No. Men
Firing
Rounds
per man
Total
Rounds
Number Rounds
% on
Target
Not
Expend.
On
Target
On
Screen
X
y
r
E. a
110
- 4.4
16*8
20.2
21.4
29.4
4
4
15
1
4
11
0.267
265
0.0
23.0
20.0
15.9
25.6
4
4
16
0
1
13
0.062
E a b
110
+ 4.0
7.9
18.0
11.3
21.3
4
4
11
5
2
7
0.182
265
+ 4*0
* 8.0
21.0
24.8
32.5
4
4
16
0
0
6
0.000
Mi c
110
- 1.8
16.7
13.4
8.7
16.0
4
4
14
2
7
14
0.500
265
- 1.4
6.9
41.1
23.5
47.3
4
4
15
1
1
8
0.067
M s d
110
- 10.8
13.0
11.6
15.4
19.3
4
4
13
3
4
10
0,308
265
- 2.7
- 7.0
15.4
19.5
24.8
4
4
16
0
3
6
0.188
- Expert Riflemen Individually Firing at Target.
E g - Expert Riflemen Simultaneously Firing at Target,
- Marksmen Individually Firing at Target,
a M g - Marksmen Simultaneously Firing at Target.
TABLE A4
.ON
COMPARISON OF OBSERVED NUMBER OF SHOTS INSIDE ZONES
BOUNDED BY CIRCLES OF RADII r t , AND r a , IN., WITH
NUMBER EXPECTED FROM BIVARIATE DISTRIBUTION WITH RADIAL
STANDARD DEVIATION a x \ AT FOUR RANGES, R, IN YD: TEST 1
(A) Experts Individually o t = 6.9 R/100 {a t in in.)
(<7 = a = 4.87 R/100, in.)
x y
R(yd) 110
205
265
310
ff r 7.6
14.1
18.3
21.4
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
r r
1 2
Obsd Exptd
r r
1 2
Obsd Exptd
r r
1 2
Obsd Exptd
r r
t 2
Obsd Exptd
0 4.1
4.1 6.3
6.3 9.0
9.0 <»
25 24
28 24
23 24
20 24
0 7.6
7.6 11.7
11.7 16.6
16.6 •»
15 20
14 20
18 20
33 20
0 9.8
9.8 15.2
15.2 21.6
21.6 oc
23 18
19 18
12 18
18 18
0 11.5
11.5 17.8
17.8 25.2
05.2 B) b
20 d 16 d
12 d 12 d
7* 1 ll d
On Screen
Off Screen
Total
P(x 2 )
P(x)
96
0
96 96
0.75
0.10
69
U a
80 80
0.01
0.66
62
10 a
72 72
0.25
0.05
47 50
25° 22°
72 72
0.5
10~ 4
(B) Exp
erts Simultaneously a T = 7.8 R/100 (<r r in in.)
{a = a =* 5.51 R/100, in.)
x y
R(yd) 110
205
265
310
a T 8.6
16.0
20.7
24.2
Zone
No* in Zone
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
r r
l .2
Obsd Exptd
r r
1 2
Obsd Exptd
r r
1 2
Ob$d Exptd
r r
1 2
Obsd Exptd
0 4.6
4.6 7.1
7.1 10.1
10.1
9 8
5 8
4 8
14 8
0 8.6
8.6 13.3
13.3 18.9
18.9 L ~
8 8
7 8
5 8
12 8
0 11.1
11.1 17.2
17.2 24.4
@4.4 B) b
7 8
5 d 5 d
2 d 5 d
0 13.0
13.0 20.1
20.1 28.5
@8,5 B) b
3 d 6 d
4 d 5 d
On Screen 24
Off Screen 8 a
Total 32 32
P(X 2 > 0.05
P(x) 0.27
26
6 a
32 32
0.75
0.17
21 24
11° 7°
32 32
0.4
0.02
19 24
13 c 8 C
32 32
0.25
0.01
a Off screen in outermost zone. *|Off screen; zone unknown.
^Outside but on screen. “Within zone and on screen.
p ( X 2 ) probability of obtaining as bad or worse fit between observed and expected numbers.
P ( X ) probability of obtaining mpi as far or farther from vertical center line of target.
ORO-T-160
101
TABLE A5
COMPARISON OF OBSERVED NUMBER OF SHOTS INSIDE ZONES
BOUNDED BY CIRCLES OF RADII r„ AND r 2 , IN., WITH
NUMBER EXPECTED FROM BIVARIATE DISTRIBUTION WITH RADIAL
STANDARD DEVIATION a f \ AT FOUR RANGES, R, IN YD: TEST 1
(A) Marksmen Individually a r = 9.0 R/100 (a in in.)
(a = a = 6.36 R/100, in.)
x y
R(yd) 110
205
265
310
a T 9.9
18.4
23.9
27.9
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
Obsd Exptd
*1 r 2
Obsd Exptd
r l r 2
Obsd Exptd
r i r 2
Obsd Exptd
0 5.3
5.3 8.2
8.2 11.7
11.7 «
18 14
10 14
11 14
17 14
0 9.9
9.9 15.4
15.4 21.8
(21.8 B) b
11 18
10, 18 h
13 d 15 d
24 d 13 d
0 12.8
12.8 19.9
19.9 28.0
(28.0 B) b
«, 18 h
18 d 18 d
20 d 14 d
12 d 12 d
0 15.0
15.0 23.2
23.2 32.9
(32.9 B) b
22 20
14 d 16 d
15 d 16 d
10 d 12 d
On Screen 56
Off Screen 0
Total 56 56
P(X*) 0.25
P(x) 0.07
58 64
14 a 8 a
72 72
10
0.07
65 62
7 a 10 a
72 72
0.3
0.02
61 64
19 a 16 a
80 80
0.9
0.7
(B) Marksmen Simultaneously = 13.0 R/100 (a r in in.)
{a = a — 9.2 R/100, in.)
x y
-R(yd) 110
205
265
310
or 14.3
r
26.6
34.5
40.3
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
r i r a
Obsd Exptd
r i r 2
Obsd Exptd
Obsd Exptd
r i *2
Obsd Exptd
0 7.7
7.7 11.9
11.9 16.9
(16.9 B) b
5 8-
7 8
9 d 8 d
9 d 6 d
0 14.3
14.3 22.2
22.2 31.4
(31.4 B) b
4 d 8 d
2 d 6 d
8 d 5 d
5 d 4 d
0 18.4
18.4 28.7
28.7 40.6
(40.6 B) b
11 8
13 d 8 d
3 d 5 d
5 d 3 d
0 21.6
21.6 33.6
33.6 47.5
(47.5 B) b
ll d 8 d
A ftd
Id Jd
S d 2 d
On Screen 30 30
Off Screen 2 a 2 a
Total 32
P( X ») 0.5
P(x) 0.3
19 23
13 a 9 a
32 32
0.1
2 x 10
32 24
0 a S a
32 32
0.01
0.6
25 20
7 a 12 a
32 32
0.2
0.8
®Off screen, zone unknown.
^Outside r x but on screen.
a Within zone and on screen.
P( X 2 ) probability of obtaining as bad or worse fit between observed and expected numbers.
P ( x ) probability of obtaining mpi as far or farther from vertical center line of target.
102
ORO-T-160
f ;
TABLE A6
COMPARISON OF OBSERVED NUMBER OF SHOTS INSIDE ZONES
BOUNDED BY CIRCLES OF RADII r„ AND r 4 , IN., WITH
NUMBER EXPECTED FROM BIVARIATE DISTRIBUTION WITH RADIAL
STANDARD DEVIATION o f AT FOUR RANGES, R, IN YD: TEST 2
(A) Experts Individually o T - 6.9 R/100 (er f in in.)
{a = o = 4.87 R/100, in.)
x y
R(yd) 110
205
265
310
o, 7.6
14.1
18.3
21.4
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
Obsd Exptd
p i r*
Obsd Exptd
r i
Obsd Exptd
r i P 2
Obsd Exptd
0 4.1
4.1 6.3
6.3 9.0
9.0 °°
15 24
23 24
22 24
36 24
0 7.6
7.6 11.7
11.7 16.6
16.6
9 16
8 16
9 16
38 16
0 9.8
9.8 15.2
15.2 21.6
21.6 B) c
20 16
14 j 16
14“ 13“
8 d ll d
0 11.5
11.5 17.8
17.8 25.2
25.2 B) c
21 20
31 20
On Screen 9 1
Off Screen 5 a
Total 96 96
P(x*) 0.02
P(x) 0.25
45
19 a
64 64
<0.001
3x10"*
56 56,
8 b 8 b
64 64
0.71
0.04
77 76
3 b 4 b
80 80
0,02
2 x 10” 9
(B) Experts Simultaneously & r = 7.8 R/100 (a t in in.)
( ff = = g,51 R/100, in.)
* y
R(yd)
110
205
265
310
°r
8.6
16.0
20.7
24.2
Zone
No. in
Zone
Zone
No. in
Zone
Zone
No. in
Zone
Zone
No. in
Zone
Ti T 2
Obsd
Exptd
r i r 2
Obsd
Exptd
r i r 2
Obsd
Exptd
P 1 p 2
Obsd
Exptd
0 4.6
6
8
0 8.6
6
16
0 14.1
10
8
0 13.0
8,
8,
4.6 7.1
8
8
8.6 13.3
10
16
11.1 17.2
9,
8,
13.0 20.1
2 d
7 d
7.1 10.1
11
8
13.3 18.9
15
16
17.2 24.2
sj
20.1 28.5
7?
ej
10.1 oo
7
8
18.9 oq
33
16
24.4 B) c
l d
6 d
28.5 B) c
8 d
5 d
On Screen
28
58
29
29,
25
26
Off Screen
4 a
6 a
4 b
3 b
7 b
6 b
Total
32
32
64
64
32
32
32
32
PCx 1 )
0.63
<0.001
0.26
0.23
P(x)
0.49
0,01
0.52
0.42
f'Off screen in outermost zone.
D Off screen, zone unknown.
P( x 1 ) probability of obtaining
P ( x ) probability of obtaining
^Outside r x but on screen.
a Within zone and on screen.
as bad or worse fit between observed and expected numbers,
mpi as far or farther from vertical center line of target.
ORO-T-160
103
si
DECLASSIFIED
TABLE A7
I
COMPARISON OF OBSERVED NUMBER OF SHOTS INSIDE ZONES
BOUNDED BY CIRCLES OF RADII r„ AND r a , IN., WITH
NUMBER EXPECTED FROM BIVARIATE DISTRIBUTION WITH RADIAL
STANDARD DEVIATION a t AT FOUR RANGES, R, IN YD: TEST 2
(A) Marksmen Individually a t = 9.0 R/100 (a t in in.)
(<7 = a = 6.36 R/100, in.)
x y
R(yd) 110
205
265
310
a r 9.9
18.4
23.9
27.9
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
i 1 r 2
Obsd Exptd
r 2
Obsd Exptd
r i *2
Obsd Exptd
r i r a
Obsd Exptd
0 5.3
5.3 8.2
8.2 11.7
11.7 ~
13 16
21 16
16 16
14 16
0 9.9
9.9 15.4
15.4 21.8
21.8 ~
9 18
9 18
12 18
42 18
0 12.8
12.8 19.9
19.9 28.1
28,1 B)°
32 24
20 24 h
27“ 20“
9 d 17“
0 15.0
15.0 23.2
23.2 32.9
32.9 B) c
13, 20
13 d 18 d
17 d 14 d
18 d 13 d
On Screen 64
Off Screen 0
Total 64 64
PCX 1 ) 0-50 _
P(x) <2 xl0“*
59
13 a
72 72
<0.001
<2xl0* 9
88 85
8 b ll b
96 96
0.04
<2 xlO -9
61 h 65
19 b 15 b
80 80
0.12
<2x10“^
(B) Marksmen Simultaneously oj. = 13.0 R/100 (ff r in in.)
(a = cr = 9.2 R/100, in.)
x y
R(yd) 110
205
265
310
o r 14.3
26.6
34.5
40.3
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
Zone
No. in Zone
*2
Obsd Exptd
*1 *2
Obsd Exptd
*1 *2
Obsd Exptd
r 2
Obsd Exptd
0 7.7
7.7 11.9
11.9 16.9
16.9 .»
13 8
9 8
3 8
7 8
0 14.3
14.3 22.2
22.2 31.4
31.4 B)°
16 16
10 , 16 d
13 d 15 d
10 d 12 d
0 18.5
18.5 28.7
28.7 40.6
40.6 B) c
13 8
8 d 6 d
3 d 5 d
0 d 5 d
0 21.6
21.6 33.6
33.6 47.5
47.5 B) c
13 8
8 d 6 d
8 H 5 d
2 d 5 d
On Screen 29
Off Screen 3 a
Total 32 32
p(x 2 > 0.09
P(x) 0.23
49 l 59
16 b 6 b
65 65
<0.001
<2 xlO” 9
24 h 24
8 b 8 b
32 32
0.05
0.04
26 24 h
6 b 8 b
32 32
0.15
0.03
^Off screen in outermost zone. ^Outside r 1T but on screen.
b Off screen, zone unknown. Within zone and on screen.
P ( ) probability of obtaining as bad or worse fit between observed and expected numbers.
P ( x ) probability of obtaining mpi as far or farther from vertical center line of target.
104
DECLASSIFIED
ORO-T-160
INFORMATION
TABLE A 8
PROBABILITIES, FOR EXPERTS FIRING INDIVIDUALLY,
OF OBTAINING EXACTLY 1, 2, 3, 4, AND 5 HITS
ON TYPE E SILHOUETTE WITH FIVE-SHOT PATTERN
SALVO FOR INDICATED TARGET RANGES
Range, yd
Exact No. of Hits
At least
1 hit
1
2
3
4
5
100
0.040
0.002
0.049
0.420
0.489
1.000
150
0.174
0.041
0.269
0.506
0.000
0.990
200
0.325
0.145
0.398
0.091
0.000
0.959
250
0.423
0.353
0.125
0.000
0.000
0.901
300
0.546
0.280
0.000
0.000
0.000
0.826
350
0.524
0.165
0.000
0.000
0.000
0.689
400
0.499
0.087
0.000
0.000
0.000
0.586
TABLE A9
PROBABILITIES, FOR MARKSMEN FIRING INDIVIDUALLY,
OF OBTAINING EXACTLY 1, 2, 3, 4, AND 5 HITS
ON TYPE E SILHOUETTE WITH FIVE -SHOT PATTERN
SALVO FOR INDICATED TARGET RANGES
Range, yd
Exact No. of Hits
At least
1 hit
1
2
3
4
5
100
0.111
0.011
0.093
0.415
0.360
0.990
150
0.271
0.066
0.250
0.350
0.000
0.937
200
0.388
0.122
0.284
0.058
0.000
0.852
250
0.434
0.240
0.085
0.000
0.000
0.759
300
0.482
0.186
0.000
0.000
0.000
0.668
350
0.436
0.108
0.000
0.000
0.000
0.544
400
0.398
0.057
0.000
0,000
0.000
0.455
; U <
^ j/ ■ . ft* V*
^ *i £ £i
THE JOHNS HOPKINS UNIVERSITY
OPERATIONS RESEARCH OFFICE
6JblO Connecticut Avenue
Chevy Chase, Maryland
a aa'^gas
18 November 1952
SUBJECT: Distribution of Project BALANCE Technical Memorandum, QR0-T-160,
"Operational Requirements for an Infantry Hand Weapon."
TO: The Deputy Assistant Chief of Staff, G-3,
for Research, Requirements and Special Weapons
Department of the Army
Room 3E37U, The Pentagon
Washington 25, D. C.
1. References:
a. Memorandum, Office of the Assistant Chief of Staff, G-3,
Operations, f?.le G-3 Oli.0 ORO, dated 22 October 1952, subject: Department
of the Army Operations Research Office Publication."
b. Letter, Office of the Assistant Chief of Staff, G-3, RR&SW,
dated 8 August 1952, subject: "Distribution List for Project BALANCE."
2. a. Pursuant to paragraph 2, a. Inclosure No. 1, reference a,
advance copies of 0R0-T-160, "Operational Requirements for an Infantry
Hand Weapon," by Norman Hitchman, Scott Forbush, and George Blakemore,
Jr., are transmitted herewith.
b. It is requested that authority be given for the distribution
of this document according to the basic Operations Research Office distri-
bution list, as supplemented by the Project BALANCE list of reference b,
and to include all the optional addressees on the latter list.
3. The findings and suggestions presented in this technical memo-
randum reflect, on the one hand, facts already experimentally determined;
and, on the other, certain emergent principles relative to the operational
effectiveness of the general issue rifle. Many of these principles re-
quire further experimentation in order conclusively to fix details of
their application. Restatement, as below, of the basic conclusions and
recommendations, to include both certain additional information as yielded
to the date of this letter by a continuing study, and also comment as to
further investigation indicated, may make clearer the extent of present
knowledge.
SI
NWCgtitATtON
Conclusions:-
Proven
Proven
Proven
Concluded from analysis;
suggested as a desirable
operational principle;
needs experimental veri-
fication.
a ,n
f « * y, i
i C ^
s^ujoi i i %j
a. Weapon employment and battlefield
visibility data, show the limiting
effect upon ranges of engagement
for the rifle of both combat practice
and terrain interruptions to the line
of sight* It is clearly established
that the relatively short ranges pre-
ponderate: "aimed 11 rifle fire is
delivered at ranges less than 300
yards about three-quarters of the
time* There is only a very limited
need for the capability for such fire
at greater ranges. Although a distri-
bution of effect which does not exclude
all capabilities at those greater
ranges is required, the weapon should
be designed to maximize hit probability
at the more common ranges. (The infre-
quent exceptions include the sniping
fire of specially trained and equipped
riflemen. —Also, it should be noted
that bearing upon the desirability of
adopting a single round for all small
arms is the need for machine-gun fire
with suitable trajectory and adequate
wounding power out to 1800-2000 yards.)
b. In the man-rifle combination, aiming
errors are generally large— far in ex-
cess of purely ballistic dispersion.
Thus, if at any extra cost, the general
purpose weapon need not be designed to
provide the current high degree of
precision.
c. The hill automatic feature, in rifles of
the usual design, and in the current US
experimental models, does not increase
the expectation of hitting separated
man-targets.
d. A controlled dispersion feature, as in-
corporated in a "salvo" automatic of the
type proposed, may largely compensate
for the large aiming errors which
typically accompany each trigger pull.
Unclassified
S!
SECUl
'RMATiON
Proven, i
at Princeton University, the
Army Chemical Center, Aber-
deen Proving Ground, and else-
where. Tests of bullets, as
contrasted with spherical
pellets, have not been ex-
tended beyond the range of
calibers .30-. 21. Additional
experimentation, through a
range extended downward, is
required to determine the best
in. i.3 it ary caliber, from 'the
standpoint of ’‘wounding power”
and other considerations.
At the cost of a small loss in armor
penetrating ability at some ranges (a
characteristic of doubtful military
value in the rifle), a weapon of a
caliber smaller than .30, providing
a correspondingly higher velocity,
offers generally superior “wounding
power" at the ranges of interest
(and somewhat beyond); improved ex-
terior ballistics; lighter ammunition;
a slightly lighter rifle i and seme
reduction in recoil. The small cali-
ber appears especially valuable in
connection with a "salvo" automatic
type of shoulder weapon which projects
four- or five-round dispersion patterns.
Caliber and other ammunition charac-
teristics within the following ranges
appear to offer promise of substantial
all-round improvement:
(1) Caliber: .276 (7mm) - .180 (U.57mm).
(2) Wt. ball: lj.0-60 gr (168 gr for cal-
iber .30, M2 AP).
(3) Wt. charge: U0-h5 gr ($3 gr for
caliber *30, M2 AP).
(li) Wt. complete round: 250-300 gr (1(16
gr for caliber .30, M2
AP).
(5) Muzzle velocity: 3700-1:800 ft per
sec (2770 ft per sec
for caliber .30, M2
AP).
(6) Muzzle energy: 1800-2200 ft-lb
(2800 ft-lb for cali-
ber .30, M2 AP).
Proven, as to lethality f.
of agent; feasibility of
incorporation in the round
is estimated from preliminary
study and expert opinion;
relative importance of disad-
vantages has not been weighed.
/ /"x*
sccu
Toxic agents could greatly increase the
lethality of bullet hits; and the in-
corporation of such agents in mass pro-
duced small aims ammunition is judged
feasible. Disadvantages such as an un-
avoidable small time delay in producing
the lethal effect, and the ease with
which the enemy could retaliate in
kind, as well as the relative desir-
ability of killing as contrasted with
RMATION
SE<
INFORMATION
wounding, would require analysis if
a policy decision sanctioning the use
of such agents were made.
Recommendations
Experiment and test for g.
determining details of
design, for verifying
engineering and pro-
duction feasibility,
and for establishing
jj t acceptability,
&:?z- necessary «
0R0 recommends the manufacture and test
of experimental weapons and ammunition
in sufficient quantity, and of a suf-
ficient range in design type, to permit
conclusive and specific determinations
with respect tos
(1) Verification of the operational
value of a pattern dispersion feature
(calculated to maximize hitting at the
ranges of concern) in a ’’salvo,” or
controlled burst cyclic, automatic*
(2) Selection of the best smaller
caliber for such a weapon, upon the
basis of all functionally associated
characteristics .
(3) The feasibility of designs which
afford the desired characteristics,
with sufficient reliability in pro-
jecting the chosen dispersion pattern,
with controlled length of burst if a
cyclic weapon, and without objection-
able cumulative recoil effects.
U. Further experimentation and test of the sort indicated need not
be very expensive nor time consuming. Certain positive information of
real importance and immediate application, long lacking in the procedures
by which military characteristics are set, and rifles and ammunition are
designed, could be provided without undue effort. Caliber, for example,
has been the subject of such prolonged controversy, is now still so dis-
puted within the NATO (despite a small, measure of agreement on the standard-
ization of ammunition wrung from the Standing Group), and has. in the past
been so often fixed by arbitrary ruling, that it is high time all the
relevant facts as to caliber and ballistics were established upon a firm
experimental basis. Again, a positive criterion of ’’wounding power” should
be found and related to tactical employment of the rifle. Finally, both the
design and performance of a shoulder weapon incorporating the novel controlled
dispersion feature should be put to actual test*
1 Incl
ORO-T-160 (copies 2 to 10)
Copies (less incl) fhmished
Director, ORO
Editor, 0R0
Mr. Norman Hitcfaaan
/s/ Edward M. Parker
Edward M ■ Parker
Chairman, Project BALANCE
SECURI
DEPARTMENT OF THE ARMY
OFFICE, ASSISTANT CHIEF OF STAFF, G-3, OPERATIONS
REGRADE D . BY AUTHOI^™™ 25 » D * °*
O F CrU#* 5Z-1 AtjL
3 Y Z O N ^/30/^ 2_
G-3 040 ORO (16 Dec 52) 8 January 1953
SUBJECT: Technical Memorandum 0R0-T-160, "Operational Requirements for
An Infantry Hand Weapon"
70: Commandant
The Army War College
Carlisle "arracks, Pennsylvania
ATTN: Librarian
1. Transmitted herewith for your advance information is one copy
of Technical Manor andum 0R0-T-160, "Operational Requirements for an
Infantry Hand Weapon."
2. This publication is a working paper of the Operations Research
Office (Project BALANCE), in which consideration is given to the desired
capabilities of a modern rifle. The Operations Research Office makes
one particular recommendation already approved by the Chief of Staff,
i.e., "that a m a.U (but adequate) number of experimental weapons, in-
corporating the desirable characteristics enumerated, be manufactured
anfl tested by the Ordnance Corps, in order more conclusively to determine
the military value of the suggested features."
3. Request that appropriate comments on this Memorandum be sub-
mitted to ACofS, G-3 (RRScSW) for consideration by the Director of the
Operations Research Office in the preparation of the final report.
FOR THE ASSISTANT CHIEF OF STAFF, G-3:
1 Incl
ORO-T-160
Brigadier General, GS
Deputy ACofS, G-3 for
Research, Requirements & Special Wpns.
UNCLASSIFIED
si
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